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

Answer:

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 = $5(x-1.50)=5(3.75-1.50)=\ 11.25$

Step-by-step 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,

$3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75$

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 = $5(x-1.50)=5(3.75-1.50)=\ 11.25$