Question

The cost of toner cartridges is 19.50 more than the cost of an ink cartridge. Colleen ordered 11 ink and 4 toner cartridges and thw total cost 460.50. Write and solve a system of equations to fons the cost of each cartridge.

Answer 1

Toner = $45.00; ink = $25.50

Explanation:

Let T = the cost of a toner cartridge and I = the cost of an ink cartridge

We have two conditions:

(1) T = I + 19.50

(2) 4T + 11I = 460.50 Substitute (1) into (2)

4(I + 19.50) + 11I = 460.50 Remove parentheses

4I + 78.00 + 11I = 460.50 Combine like terms

15 I + 78.00 = 460.50 Subtract 78.00 from each side

15I = 382.50 Divide each side by 15

(3) I = 25.50

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Substitute (3) into (1)

T = 25.50 + 19.50

T = 45.00

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Check:

(1) 45.00 = 25.50 + 19.50

45.00 = 45.00

(2) 4×45.00 + 11×25.50 = 460.50

180.00 + 280.50 = 460.50

460.50 = 460.50