Question

When the​ women's soccer team won the state​ championship, the parent boosters welcomed the team back to school with a balloon bouquet for each of the 18 players. The parents spent a total of ​$94.32 ​(excluding tax) on foil balloons that cost ​$1.94 each and latex​ school-color balloons that cost ​$0.17 each. Each player received 10 ​balloons, and all the balloon bouquets were identical. How many of each type of balloon did each bouquet​ include?

Each bouquet included
nothing foil balloons and
nothing latex balloons.

Answer 1

Each bouquet included 2 foil balloons and 8 latex balloons.

Explanation:

Let f represent the number of foil balloons in each bouquet. Then 10-f is the number of latex balloons. The problem statement tells us the cost of all of the bouquets is ...

18(1.94f +0.17(10-f)) = 94.32

We can divide by 18 to get ...

1.94f +1.70 -0.17f = 5.24

1.77f = 3.54 . . . . . . . . . . . . subtract 1.70

f = 3.54/1.77 = 2 . . . . . . . . divide by the coefficient of f

The number of latex balloons is 10-2 = 8.

Each bouquet included 2 foil and 8 latex balloons.