Question

At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but each was $1.50 less than the items that Tanya bought. Both Tanya and Tony 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 Tanya's items. (b) Solve the equation. Show your work. (c) Check your solution. Show your work. (d) State the solution in complete sentences.

Answer 1

Part a)
`3x=5(x-1.50)`

Part b)
`x=\$3.75`

Part c) see the explanation in Part c)

Part d) see the explanation in Part d)

Explanation:

Part a) Write an equation

Let

x -----> represent the cost of one of Tanya's items

y ----> represent the cost of one of Tony's items

we know that

`y=x-1.50`

Tanya bought 3 items -----> 3x

Tony bought 5 items -----> 5y----> 5(x-1.50)

If Tanya and Tony paid the same amount of money

then

The cost of three of Tanya's items is equal to the the cost of five of Tony's items

so

`3x=5(x-1.50)`

Part b) Solve the equation

we have

`3x=5(x-1.50)`

Solve for x

distribute the right side

`3x=5x-7.50`

Group terms that contain the same variable

`5x-3x=7.50`

Combine like terms'

`2x=7.50`

Divide by 2 both sides

`x=\$3.75`

Find the value of y

`y=3.75-1.50=\$2.25`

Part c) Check your solution

substitute the value of x in the originally equation

`3(3.75)=5(3.75-1.50)`

`11.25=5(2.25)`

`11.25=11.25` ----> is verified

Part d) State the solution in complete sentences

we have that

The cost of one of Tanya's items was $3.75

Tanya paid $11.25 for 3 items

The cost of one of Tony's items was $2.25

Tony paid $11.25 for 5 items

Tanya and Tony paid the same amount of money