1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Setler [38]
2 years ago
9

Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushe

s for $34. Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush. Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17. How much did each type of material cost?​
Mathematics
1 answer:
maria [59]2 years ago
7 0

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34       Eq. 1

c + 3t + b = 22           Eq. 2

3c + 2b = 17               Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7            Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17      Eq. 3

c + b = 7          Eq. 4

Solve Eq. 4 for b.

b = 7 - c        Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22           Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4

You might be interested in
What X !!!!!!!!!!!!!!!!!! Help me please!!!!
Vaselesa [24]

Answer:

<h2><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>135</u></em><em><u>°</u></em></h2>

Step-by-step explanation:

<em><u>According</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>problem</u></em><em><u>, </u></em>

45° + x = 180° <em>[</em><em>Linear</em><em> </em><em>pair</em><em>]</em>

=> x = 180° - 45°

=> <em><u>x = 135° (Ans)</u></em>

5 0
2 years ago
Read 2 more answers
Kurt has a collection of 155 United States and Canadian stamps. He has 1.5 times as many United States stamps as Canadian stamps
stealth61 [152]

Kurt has 93 United States stamps in his collection

Step-by-step explanation:

The given is:

  • Kurt has a collection of 155 United States and Canadian stamps
  • He has 1.5 times as many United States stamps as Canadian stamps

We need to find how many United  States stamps Kurt has in his collection

Assume that kart has x Canadian stamps

∵ kart has x Canadian stamps

∵ He has 1.5 times as many United States stamps as Canadian stamps

- That means the number of United States stamps is 1.5 times

   the number of the Canadian stamps

∴ The number of the United States stamps = 1.5 x

∵ Kurt has a collection of 155 United States and Canadian stamps

- Add the two numbers of stamps and equate the answer by 155

∴ x + 1.5 x = 155

- Add like terms

∴ 2.5 x = 155

- Divide both sides by 2.5

∴ x = 62

∵ The number of United States stamps = 1.5 x

∴ The number of United States stamps = 1.5(62)

∴ The number of United States stamps = 93 stamps

Kurt has 93 United States stamps in his collection

Learn more:

You can earn more about the simple equation in brainly.com/question/11306893

#LearnwithBrainly

5 0
3 years ago
Find the slope of a line
Dvinal [7]

Answer:

1 is the slope.

Step-by-step explanation:

I did this math question on edge.

8 0
3 years ago
Solve the initial-value problem<br><br> y' = x^4 - \frac{1}{x}y, y(1) = 1.
natta225 [31]

The ODE is linear:

y'=x^4-\dfrac yx

y'+\dfrac yx=x^4

Multiplying both sides by x gives

xy'+y=x^5

Notice that the left side can be condensed as the derivative of a product:

(xy)'=x^5

Integrating both sides with respect to x yields

xy=\dfrac{x^6}6+C

\implies y(x)=\dfrac{x^5}6+\dfrac Cx

Since y(1)=1,

1=\dfrac16+C\implies C=\dfrac56

so that

\boxed{y(x)=\dfrac{x^5}6+\dfrac5{6x}}

4 0
3 years ago
Which system of equations has exactly one solution?
tester [92]

Answer: Most of them cross each other once so I am not sure which one is the answer (sorry)

Step-by-step explanation:

x+y=7 is parallel to 3x+3y=3 and -6x-6y=3

3x+y=-1 and 6x+2y=-2 have infinite solutions togther (both are on top of each other)

The rest of the ways cross each other once

8 0
2 years ago
Other questions:
  • Drag the orange point on the cube to change its side length. Then set the base of the pyramid to the same dimensions as a face o
    6·2 answers
  • 8 times what equals 40
    15·2 answers
  • 12. State whether the number 97 is prime, composite, or neither.
    11·1 answer
  • Which aet of processes must occur to form soil​
    5·1 answer
  • In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per
    12·1 answer
  • Need help with these answer please and thank you..​
    8·1 answer
  • How to solve including answer; 9r^2 +30r +25=0 by factoring
    5·1 answer
  • A line with a slope of 1/2 passes through the point (2, -1) what is the Equation of the line​
    6·1 answer
  • In a game the player wins if he rolls a 6 on a number cube. If the number cube is rolled 18 times, then what is a reasonable pre
    10·1 answer
  • PLEASEEEEE SURELY SOMEBODY OUT THERE MUST KNOW HOW TO DO THIS FREAKIN HARDD COMPLICATED MATHHH PLSSS HELPPP MEEEEEEEEEEEEEEEEEEE
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!