At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 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 ? (a) Write an equation. Let x represent the cost of one of Spongebob’s items.

(b) Solve the equation. Show your work.

(c) Check your solution. Show your work.

(d) State the solution in complete sentences.

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(a) The equation is 3 × x = 5 × (x - 1.5)

(b) The price of each item Spongebob bought is $3.75

The price of each item Patrick bought is $2.25

(c) The total cost of the items bought by Spongebob = $11.25 = The total cost of the items of items bought by Patrick bought

(d) The prices of the 3 items that Spongebob bought are $3.75 each. The prices of the 5 items that Patrick bought are $2.25 each  

Step-by-step explanation:

The given parameters are;

The number of items Spongebob bought = 3 items

The price of each item Spongebob bought = The same = x

The number of items Patrick bought = 5 items

The price of each item Patrick bought = Equal price = x - 1.5

The amount of money Spongebob paid = The amount of money Patrick paid

(a) Therefore, the equation with representing the expressions are;

The total price Spongebob paid = (The number of items Spongebob bought) × (The price of each item Spongebob bought)

The total price Spongebob paid = 3 × x

The total price Patrick paid = (The number of items Patrick bought) × (The price of each item Patrick bought)

The total price Patrick paid = 5 × (x - 1.5)

The equation is 3 × x = 5 × (x - 1.5)

(b) From the following equation;

The amount of money Spongebob paid = The amount of money Patrick paid

We have;

3 × x = 5 × (x - 1.5)

3 × x = 5 × x - 7.5

7.5 =  5 × x - 3 × x = 2 × x

x = 7.5/2 = 3.75

x = $3.75

Therefore;

The price of each item Spongebob bought = x = $3.75

The price of each item Spongebob bought = $3.75

The price of each item Patrick bought = x - 1.5 = $3.75 - $1.5 = $2.25

The price of each item Patrick bought = $2.25

(c) We check the total cost of the items of items bought by Spongebob as follows;

The total amount of cost of the items bought by Spongebob = 3 × $3.75 = $11.25

The total cost of the items of items bought by Spongebob = $11.25

The total cost of the items of items bought by Patrick bought = 5 × $2.25 = $11.25

The total cost of the items of items bought by Patrick bought = 5 × $2.25 = $11.25

The total cost of the items of items bought by Patrick bought = $11.25

From which we have;

The total cost of the items bought by Spongebob = $11.25 = The total cost of the items of items bought by Patrick bought

(d) The prices of the 3 items that Spongebob bought are $3.75 each. The prices of the 5 items that Patrick bought are $2.25 each.

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step-by-step explanation: