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.

Let us assume Brian's one item cost = $ x.

Chris one item cost is $2.50 more than Brian’s items each cost.

Therefore, Chris one item cost is = $(x+2.50).

Total cost of Brian's 4 items = 4*x = 4x.

Total cost of Chris's 3 itmes = 3*(x+2.50) =3(x+2.50)

It is said that Brian and Chris both paid the same amount of money.

Therefore,

Total cost of Brian's 4 items = Total cost of Chris's 3 itmes.

a) We can setup an equation now,

b) Let us solve above equation for x.

4x = 3(x+2.50)

distributing 3 over (x+2.50), we get

4x = 3x + 7.50.

Subtracting 3x from both sides we get

4x-3x = 3x-3x =7.50.

Therefore, the cost of one of Brian's items = $7.50.

Chris one item cost is $2.50 more than Brian’s items each cost.

Chris one item cost is = 7.50 +2.50 = $10.00.

c) Plugging x=7.50 in the equation we get to check the solution.

4x = 3(x+2.50)

4(7.50) = 3(7.50+2.50).

30 = 3(10.00)

30=30.

Therefore, solution x=7.50 is correct.