Question

The owner of a music store ordered merchandise with a total value of $11000 from her supplier. She ordered CDs costing $10 each and DVDs costing $20 each. If she ordered 200 more CDs than DVDs, how many of each did she order?

Answer 1

500 CDs and 300 DVDs.

Explanation:

Given:

The owner of a music store ordered merchandise with a total value of $11000 from her supplier.

She ordered CDs costing $10 each and DVDs costing $20 each.

If she ordered 200 more CDs than DVDs.

Question asked:

How many of each did she order?

Solution:

Let number of DVDs ordered by her =
`x`

Then the number of CDs ordered by her =
`x+200`

Cost of 1 CD = $10

Cost of
`x+200` CDs =
`10(x+200)=10x+2000`

Cost of 1 DVD = $20

Cost of
`x` DVD =
`20x`

Total value of her ordered = $11000

Cost of
`x+200` CDs + Cost of
`x` DVDs = $11000

`10x+2000+20x=11000\\ \\ 30x+2000=11000\\ \\ Subtracting\ both\ sides\ by\ 2000\\ \\ 30x+2000-2000=11000-2000\\ \\ 30x=9000\\ \\ Dividing\ both\ sides\ by \ 30 \\ \\ x=300`

Number of DVDs ordered by her =
`x` = 300

Number of CDs ordered by her =
`x+200` = 300 + 200 = 500

Therefore, she ordered 500 CDs and 300 DVDs from her supplier.