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. 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.

hurry !!

Answer 1

(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

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.