Question

Write a system of equations from the following scenario

Marco went a sports shop and purchased 3 soccer balls, 1 set of
baseballs, and a case of golf balls for $77.50. Todd bought 3
soccer balls and 2 cases of golf balls for $67.50. Matt bought 1 set
of baseballs and 3 cases of golf balls for $70. Write a system of
equations that could be used to determine the cost of each item
then determine the cost of each item.

Answer 1

To find the cost of each item in the sports shop scenario, we define variables for each item's cost and set up a system of linear equations based on the purchases made by Marco, Todd, and Matt. We then solve the system using elimination or substitution methods to obtain the prices for the soccer ball, set of baseballs, and case of golf balls.

Step-by-step explanation:

To solve the system of equations for the cost of each item in the sports shop scenario, let's denote:

• S as the price of one soccer ball,
• B as the price of one set of baseballs,
• G as the price of one case of golf balls.

According to the scenario, the following equations represent the purchases:

1. Marco's purchase: 3S + B + G = $77.50
2. Todd's purchase: 3S + 2G = $67.50
3. Matt's purchase: B + 3G = $70

We can solve this system of linear equations using substitution or elimination methods. Let's use elimination:

1. From Todd's purchase, express S in terms of G: S = ($67.50 - 2G)/3
2. Substitute S into Marco's equation: B + G + 3(($67.50 - 2G)/3) = $77.50, which simplifies to B + G = $77.50 - $67.50
3. Now we have B + G = $10 and from Matt's purchase we know B + 3G = $70.
4. Subtract the first from the second equation to solve for G, then use the value of G to find B in Matt's equation, and finally use the values of B and G to find S in either Marco's or Todd's equation. ...