Question

3. 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?

Answer 1

Answer: Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

Explanation:

Let x be the cost of each item bought by Spongebob.

Then, cost of each item bought by Patrick = x- 1.50

Then, cost of 3 items bought by Spongebob = 3x

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

If both Spongebob and Patrick paid the same amount of money then

Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $2.5-$1.5=$1

Hence, Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

Answer 2

Answer: Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

Explanation:

Let x be the cost of each item bought by Spongebob.

Then, cost of each item bought by Patrick = x- 1.50

Then, cost of 3 items bought by Spongebob = 3x

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

If both Spongebob and Patrick paid the same amount of money then

`3x= 5(x-1.5)\\\\\Rightarrow\ 3x=5x-1.5*5\\\\\Rightarrow\ 3x=5x-7.5\\\\\Rightarrow\ 5x-2x=7.5\\\\\Rightarrow\ 3x=7.5\\\\\Rightarrow\ x=(7.5)/(3)\\\\\Rightarrow\ x=2.5`

Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $2.5-$1.5=$1

Hence, Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1