Question

Help Brian and Chris went together to Target to find party favors for a birthday party they are throwing together.

Brian found 4 items that cost the same amount. Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. Brian and Chris both 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 Brian's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
Answer:

Answer 1

(a) Let x be the cost of one of Brian's items, then cost of all 4 items bought by Brian will be 4x.

We have been given that Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. The price of each item bought by Chris will be x+2.5. Therefore, the cost of all 3 items bought by Chris will be
`3(x+2.5)`.

(b) We are told that Brian and Chris both paid the same amount of money, so we can equate costs of Brian's 4 items and Chris's 3 items as:

`4x=3(x+2.5)`

Now let us solve for x by distributing 3.

`4x=3x+7.5`

`4x-3x=7.5`

`x=7.5`

Therefore, cost of Brian's each item is $7.5.

Now let us find price of Chris's each item.

`\text{Cost of Chris's each item}=x+2.5=7.5+2.5=10`

Therefore, cost of Chris's each item is $10.

(c) Now let us check our solution by substituting x=7.5 in
`4x=3(x+2.5)`.

`4(7.5)=3(7.5+2.5)`

`4(7.5)=3(10)`

`30=30`

We can see that both Brian and Chris spent equal amount of money that is $30, therefore, our solution is correct.