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, volleyball balls for $11.99 each, and kneepads 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.

a) Let U be the number of uniforms and B be the number of volleyball balls purchased. The system of equations is:
U + B = 55
18.50U + 11.99B + 9.75(6) = 703.55

b) Let X be the number of uniforms and Y be the number of volleyball balls purchased. The system of equations is:
X + Y = 55
18.50X + 11.99Y + 9.75(6) = 703.55

c) Let U be the number of uniforms and B be the number of volleyball balls purchased. The system of equations is:
U + B = 703.55
18.50U + 11.99B + 9.75(6) = 55

d) Let X be the number of uniforms and Y be the number of volleyball balls purchased. The system of equations is:
X + Y = 703.55
18.50X + 11.99Y + 9.75(6) = 55

Answer 1

The variables and system of equations to represent the situation are defined correctly. The variables U and B represent the number of uniforms and volleyball balls purchased, and the system of equations U + B = 55 and 18.50U + 11.99B + 9.75(6) = 703.55 accurately represent the given information and constraints.

Step-by-step explanation:

The system of equations that represents the situation is:

Let U be the number of uniforms and B be the number of volleyball balls purchased.

Equation 1: U + B = 55

Equation 2: 18.50U + 11.99B + 9.75(6) = 703.55

In equation 1, U represents the number of uniforms and B represents the number of volleyball balls. The sum of U and B should be equal to 55, as there are 55 items purchased in total.

In equation 2, the total cost of the uniforms, volleyball balls, and kneepads should be equal to the budget of $703.55. The cost of uniforms is $18.50 each, the cost of volleyball balls is $11.99 each, and there were 6 more balls purchased than uniforms.