Joel needs to buy some blank DVDS and zip disks to back up a large amount of data that has been generated by an accounting firm. He buys 6 DVDS and 3 zip disks for $96. He later realised these are not sufficient and so guys another 5 DVDS and 4 zip disks for $116. How much did each DVD and each Zip disk cost? (Assume the rate per item was changed for each visit). Show working.

Question

Mathematics

Amelia Cherry

24 August, 20:55

Joel needs to buy some blank DVDS and zip disks to back up a large amount of data that has been generated by an accounting firm. He buys 6 DVDS and 3 zip disks for $96. He later realised these are not sufficient and so guys another 5 DVDS and 4 zip disks for $116. How much did each DVD and each Zip disk cost? (Assume the rate per item was changed for each visit). Show working.

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Answers (1)

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Antony Finley · Answer 1

D = 4, Z = 24

Step-by-step explanation:

6D+3Z = 96

5D+4Z = 116

multiply top by 5 and bottom by - 6

top equation = 30D+15Z = 480

bottom equation = - 30D-24Z = - 696

Cancel 30D and - 30 D

top equation = 15Z = 480

Bottom equation = - 24Z = - 696

15Z - 24 Z = 480 - 696

-9Z = 216

Z = 216/9

Z = 24

Now that we have the value of Z, we can substitute it in any equation to find D

6D + 3 (24) = 96

6D + 72 = 96

6D = 96 - 72

6D = 24

D = 24/6

D = 4