Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 3 small baskets and 5 large baskets, using a total of 109 pieces of fruit. Using wire baskets, the employee assembled 9 small baskets and 5 large baskets, using a total of 157 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include
x
pieces and the large ones each include
x
pieces.

Answer 1

Let x be the number of pieces of fruit in each small basket and y be the number of pieces of fruit in each large basket. Then, we can write the following system of equations to represent the given information:

3x + 5y = 109 (using wicker baskets)
9x + 5y = 157 (using wire baskets)

To solve this system, we can use the substitution method. Solving the first equation for y, we get:

y = (109 - 3x)/5

Substituting this expression for y into the second equation, we get:

9x + 5((109-3x)/5) = 157

Simplifying and solving for x, we get:

9x + 109 - 3x = 157
6x + 109 = 157
6x = 48
x = 8

Therefore, each small basket includes 8 pieces of fruit, and each large basket includes:

y = (109 - 3x)/5 = (109 - 3(8))/5 = 17

So, the small baskets each include 8 pieces and the large ones each include 17 pieces.