John and his friends bought pastels, brushes, and canvases at an art supply store. The table shows the numbers of items bought and the amount each person spent. Identify the price of each item.

Cost of one canvas $1, one brush $2 and one pastel $3

Step-by-step explanation:

John and his friends bought pastels, brushes and canvases at an art supply store.

Let the price of each pastel represents by 'p', each brushes represents by 'b' and each canvas represents by 'c'.

John purchased 3 pastels, 4 brushes and 5 canvases for $22. The equation will be,

3p + 4b + 5c = 22 (1)

Robin purchased 2 pastels 5 brushes and 7 canvases for $23. The equation will be,

2p + 5b + 7c = 23(2)

Andrew purchased 4 pastels, 3 brushes and 6 canvases for $24. The equation will be,

4p + 3b + 6c = 24(3)

Now multiply equation (1) by 2 and equation (2) by 3.

6p + 8b + 10c = 44 (4)

6p + 15b + 21c = 69(5)

After subtracting from equation (5) to (4)

7b + 11c = 25 (6)

multiplying equation (2) by 2

4p + 10b + 14c = 46(7)

subtracting equation (3) from equation (7)

7b + 8c = 22

and subtracting from equation (6)

3c = 3

c = 1

putting the value of c in equation (6)

7b + 11(1) = 25

7b + 11 = 25

7b = 25 - 11

7b = 14

b = 2

Put the value of c and b in equation (1)

3p + 4(2) + 5(1) = 22

3p + 8 = 22 - 5

3p = 17 - 8

3p = 9

p = 3

Cost of one canvas $1, one brush $2 and one pastel $3.

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step-by-step explanation:

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