Question

Klay and Aspyn love to play in the snow with their cousins Gage and Emma. They decide to have a contest to see which team can create the most snowballs in half an hour. Because Klay and Aspyn are younger, they are allowed a 4-snowball head start. Together they can make 2 snowballs every 5 minutes. Gage and Emma are older and can make 1 snowball every 2 minutes.

Write a system of equations for this scenario.

Answer 1

The system of equations for the snowball-making contest is x = 2/5 × 30 + 4 for Klay and Aspyn, and y = 1/2 × 30 for Gage and Emma.

Step-by-step explanation:

To determine the system of equations for the snowball-making contest, let's define the following variables: Let x represent the number of snowballs Klay and Aspyn make, and let y represent the number of snowballs Gage and Emma make.

Klay and Aspyn are given a 4-snowball head start and can make 2 snowballs every 5 minutes for 30 minutes. Therefore, the equation for their snowball production over 30 minutes, taking into account the head start, is:

x = (2 snowballs / 5 minutes) × (30 minutes) + 4 snowballs

On the other hand, Gage and Emma can make 1 snowball every 2 minutes for the same duration of 30 minutes. The equation for their snowball production is:

y = (1 snowball / 2 minutes) × (30 minutes)

These two equations make up the system of equations for the snowball contest:

1. x = 2/5 × 30 + 4
2. y = 1/2 × 30