Question

The school athletic director had a budget of $703.55 to purchase 55 items for the volleyball team. He purchased uniforms for $18.50 each, volleyballs for $12.99 each, and knee pads for $9.75 per pair. He purchased six more balls than uniforms. Define the variables and write a system of equations to represent the situation.

Answer 1

Variables are x, y, z

System of equations are;

2x + z = 49

31.49x + 9.75z = 625.61

Explanation:

Let x represent uniforms, y represent volleyball, z represent a pair of knee pads.

We are told he bought 6 more balls than uniforms. Thus; y = x + 6

Since he is buying 55 items, thus equation that represents total number of items bought is;

x + y + z = 55

Since y = x + 6, then;

x + x + 6 + z = 55

2x + z = 49

We are told he purchased uniforms for $18.5 each, volleyball for $12.99 dollar each, knee pads for $9.75 dollar for each pair

Since he has a budget of $703.55.

Thus, equation that represents budget and amount for each item is;

18.5x + 12.99(x + 6) + 9.75z = 703.55

18.5x + 12.99x + 77.94 + 9.75z = 703.55

31.49x + 9.75z = 703.55 - 77.94

31.49x + 9.75z = 625.61