You sell small and large candles at a craft fair. Small candles cost $4 each and large candles cost $6 each. You collect $144 after selling a total of 28 candles. How many of each type of candle did you sell? Write a linear system to represent the situation. Be sure to define your variables.

Answers

Answer 1

Answer: Small Candle = 12, Large Candle = 16

Step-by-step explanation:

Equation is this, s+l=28 2nd equation is 4s+6l=144

now you multiply every number in the second equation by -6 since positive 6 is the second equations second constant. Now you got -6s-6l=-168 And 4s+6l=144. The -6l and positive cancel so now you got -6s + 4s = -168+144. Now you got -2s = -24. Divide them both by negative two then you get s = 12. 28 candles total - 12 = 16 so 16 large candles and 12 small. L = large candles, S = small candles.

Answer 2

Answer:

8 small candles

16 large candles

Step-by-step explanation:

1. Approach

Set up a system of equations to solve this problem. Call the number of small candles sold (x), and the number of large candles sold (y). Have one expression model the amount of money earned, the other model the number of candles sold. Then, solve this system of equations using the process of elimination. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate. Then one can solve for the other variable, and finally, substitute the value of the variable that one found back into one of the equations, and solve for the value of the other variable.

2. Set up a system of equations

Use the given information to set up a system of equations to describe the amount earned, and the amount sold

x + y = 28 -> amount sold

4x + 6y = 144 -> amount earned

3. Solve the system

As explained above, the process of elimination is a method of solving a system of equations. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate.

x + y = 28 (*-4)

4x + 6y = 144

-4x - 4y = -112

4x + 6y = 144

___________

2y = 32

/2     /2

y = 16

4. Solve to find out how much of the other candle was sold

Now back solve, substitute the found value into one of the equations, and solve to find the other value

x + y = 28

y = 16

x + 16 = 28

    -16     -16

x = 8


Related Questions

How many square feet of outdoor campot will we need for this hole?​

Answers

Answer:

10 ft. should be the answer if I did it correctly

Step-by-step explanation:

CAN SOMEONE PLEASE HELP ME I NEED THIS ASAP

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The answer is y=-2/2+3

The equation -3x + 7 = y represents the relationship between x, the time that a car drives in hours, and y, the distance the car drives in miles for car A. Identify the unit rate for this situation. <——————————————— Can someone help me on this please :/

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Answer:

here... I want to help so if your real stuck, then use this app...

Step-by-step explanation:

https://photomath.app/en/

HELP ME PLS
i’ll mark brainlist

Answers

Answer:

14.3 yds.

Step-by-step explanation:

c=√a^2 +b^2

c=√14^2 +3^2

c=√=196+9

c=14.31782106327

c=14.3 yds.

Answer:

XZ = 14.32 yd

Step-by-step explanation:

Use the Pythagorean theorem

14^2 + 3^2 = XZ^2

196 + 9 = XZ^2

XZ^2 = 205

XZ = 14.32 yd

What is the probability of rolling an even number on a number cube containing numbers 1 through 6? *

Answers

Answer:

[tex]\frac{1}{2}[/tex] or 50%

Step-by-step explanation:

Cube has 6 sides = 3 odds and 3 even

probability is found using

[tex]\frac{number of favourable outcomes}{number of total outcome}[/tex] which is [tex]\frac{3}{6} or \frac{1}{2}[/tex]

1/2 = 50%

What is the area of a semicircle that has a radius of 20 feet?

Answers

Answer:

[tex]200\pi[/tex] or 628.3185

Step-by-step explanation:

Area of a semicircle is equal to [tex]\frac{\pi r^{2}}{2}[/tex]. So, when the radius is 20, the area of the semicircle will be [tex]\frac{\pi (20)^{2} }{2} =\frac{400\pi }{2} =200\pi =628.3185[/tex].

hey guy i need help on this

Answers

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step:

[tex](12 - 9)^{2} + \frac{15}{3} \\ (3) ^{2} + \frac{15}{3} \\ 9 + \frac{15}{3} \\ 9 + 5 \\ = 14[/tex]

Solve for X
Potential answers are (WILL GIVE BRAINLIEST
1. 0
2. 11.4
3. 16
4. -16

Answers

Answer:

3)  16

Step-by-step explanation:

these are alternate-interior angles which are congruent

10x-23 = 137

10x = 160

x = 16

The measures of the angles of Triangular garden are in the ratio 2:5:5. What are the measures of the angles? Classify the triangle based on its sides :)

Answers

2x + 3x + 5x = 180

 

10x = 180

 

x = 18

 

2x = 36, 3x = 54, 5x = 90

 

They add up to 180 (definition of sum of angles of a triangle.)

PLEASE HELP THIS IS DUE IN 20 MINUTES

Describe fully the single transformation that maps shape A onto shape B.
y
4
A
2
1
B
-5 -4 -3 -2 -1 0
-1
1
2 3 4
X
5
-2
-3
-41
Total marks: 2

Answers

Answer:

I think shape A is just reflected, and make Shape B.

The reflection line is on 2 of the y axis

Step-by-step explanation:

my question is in the photo

Answers

Answer:

all the answers are there in safari can  just check it

Step-by-step explanation

a jogger runs 8 miles north and then 5 miles west what is the shortest distance to the nearest tenth of a mile he must travel to return to his starting point​

Answers

C=9.4 Miles hope this helps

An amusement park reduced its admission price to $15.50 per day, but now charges $1.50 per ride. Mark has $26 to spend on admission and rides. Write and solve an equation to find how many rides Mark can ride in one day.

Answers

Equation (26.00-15.50) ÷1.50

Answer 7 rides

Solve $26 minus $15.50 equal $10.50 then divide 10.50 by 1.50 and you’ll get 7


Al and Tom are painting a shed. Working alone, Al can paint the shed in 2 hrs. Together they can paint the shed in 1.5 hours. How long would it take Tom to paint the shed on his own?

Answers

Answer:

6 hours.

Step-by-step explanation:

The formula sort of has to be invented.

Al

rate = 1 shed / 2 hours

Tom

rate = 1 shed / x hours.

Together.

rate = 1 shed / 1.5 hours.

Equation

1 shed / 2 hours + 1 shed / x hours = 1 shed / 1.5 hours.

1/2 + 1/x = 1/1.5          Put the fractions over a common denominator.

(x + 2) / 2x = 1 / 1.5   Cross Multiply

1.5(x + 2) = 2x           Remove the Brackets.

1.5x + 3 = 2x             Subtract 1.5x from both sides

3 = 2x - 1.5x

3 = 0.5x                    Multiply both sides by 2

6 = x

It would take Al 6 hours to do the shed on his own.

4. Which trigonometric expression is equal to cos 72°? A. cos 55° B. cos 50° C. sin 61° D. sin 18°​

Answers

Answer:

D.  sin 18°

Step-by-step explanation:

sin 18 because 18 + 72 = 90

What is the change in Greenland's ice from 2010
to 2011?
Is the change positive or negative?

Answers

Answer:

negatively, the more the ice melts the high the sea level rises.

Step-by-step explanation:

from 2010 to 2011 the average ice mass decreased by 463 gigatons

Find the output, b, when the input, a, is 6.
b=17a

Answers

I think 11 hope this is the answer

if x,y are in inverse proportion then complete the following table x= 42 y=-15 , x=30 y=-----

Answers

Answer:

when x=30, y = -21

Step-by-step explanation:

x = k/y

x = 42 y = -15

x = k/y

42 = k/-15

Cross product

42 * -15 = k

-630 = k

k = - 630

Find y when x=30

x = k/y

30 = -630/y

Cross product

30 * y = - 630

30y = - 630

y = - 630/30

y = -21

when x=30, y = -21

If we have a conversion factor given to us in a fraction form that cannot be represented as an easy decimal, what can we do?

a. Conclude that the units cannot be converted to one another.
b. Assume the conversion factor is 1.
c. Attempt to use a conversion factor for different units of measurement.
d. Leave the conversion factor in fraction form.

Answers

Answer:

D) Leave the conversion factor in fraction form

Step-by-step explanation:

Leave the conversion factor in fraction form, when fraction form that cannot be represented as an easy decimal. The correct option is option D.

What is conversion Factor?

A conversion factor is a ratio expressed as a fraction that equals 1. When we use conversion factors to convert units, we multiply our original measurement by the conversion factor to get the same measurements expressed in new units.

If we have a conversion factor given to us in a fraction form that cannot be represented as an easy decimal. Leave the conversion factor in fraction form.

Because there are two type of decimals:

Terminating decimal expansion means the decimal expansion of a number which stops after a certain number of decimal places. For example, if we divide 100 by 16, the answer comes out as 6.25.Since the number of decimal place in 6.25 is 2,i.e., it stops after a certain number of decimal places, it is called a terminating decimal expansion.

On the other hand, if the decimal expansion of a number does not stop at all, then it is called a non-terminating decimal expansion. For example, if we divide 100 by 7, then the answer comes out to be 14.28571428571…….. . The decimal expansion does not stop. This is known as a non-terminating decimal expansion.

In general, if a fraction has a denominator of the form 2^n*5^m, where m and n are non-negative integers, then it will have a terminating decimal expansion. For example, 100/16 has denominator 16 which is of the form 2^4*5^0, so it has a terminating decimal expansion.

If a fraction has a denominator which is not of the form 2^n*5^m, where m and n are non-negative integers, then it will have a non-terminating decimal expansion. For example, 100/7 has a denominator 7 which is not of the form 2^n*5^m so it has a non-terminating decimal expansion.

Hence, Leave the conversion factor in fraction form, when fraction form that cannot be represented as an easy decimal.

Learn more about Fractions:

https://brainly.com/question/10354322

#SPJ2

5-(-2)= helpppp pleaseee

Answers

Answer:

7

Step-by-step explanation:

5-(-2) equals 7

das the answer 7

What is the volume, in cubic cm, of a cylinder with a height of 16cm and a base radius of 3cm, to the nearest tenths place?

Answers

Answer:452

Step-by-step explanation:

V = π r^2 h

= 3.14 * 3^2 * 16

= 3.14 * 9 * 16

= 452.16

Circle A has center of (6, 7), and a radius of 4 and circle B has a center of (2, 4), and a radius of 16.

Answers

Answer:

See solutions below

Explanation

We are to find the equation of circle A and B

The equation of a circle is expressed as;

(x-a)^2 + (y-b)^2 = r^2

(a, b) is the centre and r is the radius

For Circle A that has center of (6, 7), and a radius of 4

Substitute;

(x-6)^2 + (y-7)^2 = 4^2

(x-6)^2+(y-7)^2 = 16

Hence the equation of circle A is (x-6)^2+(y-7)^2 = 16

For circle B:

If circle B has a center of (2, 4), and a radius of 16

The equation is expressed as;

(x-2)^2+(x-4)^2 = 16^2

(x-2)^2+(x-4)^2 = 256

Hence the required equation is (x-2)^2+(x-4)^2 = 256

v/8=2
It's a one-step equation. How do I solve it?

Answers

Answer:

           Mutiplying both sides by 8

(v/8)×8 = v    and  2×8=16 so:

v/8 = 2

v = 16

Answer:

v = 16

Step-by-step explanation:

8 x 2 = 16

16/8 = 2

so v =16

35 POINTS // URGENT

On the first day of a sale, a camera was reduced by $21.60. This represented 12% off the original price. On the last day of the sale, the camera was sold for 70% of the original price. What was the final selling price of the camera?

GIVING BRAINLIEST to best explained answer. If you respond with an irrelevant answer I will report the question and your answer and your points will be taken away.

Answers

Answer:

54$ is the final selling price of the camera.

Hope this helps :)

the lengths of the sides of a triangle are 2n, n^2 and n+5 for what value of n do these lengths not make a triangle ?

Answers

The length , explain that againnnnnnn

Answer:

Step-by-step explanation:

Try n = 2

2n = 4

n^2 = 4

n+5 = 7   That works. It will make a triangle since the 2 smallest numbers are bigger than 7

Try n = 3

2n = 6

n^2 = 9

n + 5 = 8     That works. Same reason as above.

n = 4

2n = 8

n^2 = 16

n + 5 = 9    That works. Same reason.

n = 5

2n = 10

n^2 = 25

n+5 = 10   Aha! That doesn't work. the two smaller numbers only = 20.

There are likely many numbers that don't work. I'll try one more

n = 6

2n = 12

n + 5 = 11

n^2 = 36   This won't work either. Same reason as n = 5.

A city has a population of 220,000 people. Suppose that each year the population grows by 3.75%. What will the population be after 9 years? How many people

Answers

Answer:

294250 people will be there after 9 years if the population is increased 3.75% annually.

Step-by-step explanation:

First, 3.75% of 220000

then multiply the answer with 9.

again add the answer with 220000.

hence your answer came.

try it. Hope it helps

✨✨Answer number 7please ✨✨

Answers

Answer: A

Step-by-step explanation: This is a rotation. An easy way to tell the difference between a rotation and a reflection is that the order of the points will not change in a rotation. For this problem, pre-image ABCD is still in the order of ABCD when mapped to the image. (You can still follow along the points in that order). When something is reflected, the points swap orders and you would not be able to follow the points in order.

Now that we know this is a rotation, Notice A’ B’ C’ and D’ are all left of the pre-image. This means the mapped image moves counter clockwise.

The length of a picture frame is inches more than the width. For what values of x is the perimeter of the picture frame greater than ​inches?

Answers

9514 1404 393

Answer:

  x > 35

Step-by-step explanation:

The perimeter is twice the sum of length and width. You want x such that ...

  P > 156

  2(x +(x+8)) > 156

  4x +16 > 156 . . . . . simplify

  x +4 > 39 . . . . . . . . divide by 4

  x > 35 . . . . . . . . . . . subtract 4

The perimeter of the frame will be greater than 156 inches for x > 35.

PLEASE HELP MEEEEE!!!!!

Answers

Answer:

24/25 = 0.96

Step-by-step explanation:

there ya go XD

24/25=0.96
and it’s bc i rounded it

Indicar el número entero que corresponde a cada
situación

a) Se realiza un descuento de $20 en la primera compra con tarjeta de crédito.


b) Se acredita $15 al saldo telefónico por una promoción.

c) La playa de estacionamiento se encuentra en el tercer subsuelo

.
d) María Angélica tiene una deuda de $300.

e) En el nordeste de Francia la temperatura llegó a los 15 grados
bajo cero.

f) La empresa disminuyó las ventas en un promedio de 5 000
unidades por mes.

Answers

Answer:

a)-20

b)+15

c)-3

d)-300

e)-15

f)-5000

g)-400

h)-250

i)+420

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