Question

At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 items that each cost the same amount, but each was $1.50 less than the items that Spongebob bought. Both Spongebob and Patrick paid the same amount of money. What was the individual cost of each person's items?

Write an equation. Let x represent the cost of one of Spongebob's items.

Solve the equation. Show your work.

Check your solution. Show your work.

State the solution in complete sentences.

Answer 1

Cost of each item bought by Spongebob
`=x=\$3.75`

Cost of items bought by Spongebob =
`3x=3(3.75)=\$11.25`

Cost of each item bought by Patrick
`=x-1.50=3.75-1.50=\$2.25`

Cost of items bought by Patrick =
`5(x-1.50)=5(3.75-1.50)=\$11.25`

Explanation:

Let
`x` denotes cost of each item bought by Spongebob.

Number of items bought by Spongebob = 3

So,

Cost of items bought by Spongebob =
`3x`

Cost of each item bought by Patrick =
`x-1.50`

Number of items bought by Patrick = 5

Cost of items bought by Patrick =
`5(x-1.50)`

Both Spongebob and Patrick paid the same amount of money.

So,

`3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=(7.5)/(2) \\x=3.75`

So,

Cost of each item bought by Spongebob
`=x=\$3.75`

Cost of items bought by Spongebob =
`3x=3(3.75)=\$11.25`

Cost of each item bought by Patrick
`=x-1.50=3.75-1.50=\$2.25`

Cost of items bought by Patrick =
`5(x-1.50)=5(3.75-1.50)=\$11.25`