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

Answer:

Toner = $45.00; ink = $25.50

Step-by-step 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

=====

Substitute (3) into (1)

T = 25.50 + 19.50

T = 45.00

=====

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