ABC Game store sells new games, n, for $19 and used games, u, for $9. The store earned $7500 in revenue last month. The store sold 4 times as many used games as new games. Write a system of equations that represents this scenario.

Question

ABC Game store sells new games, n, for $19 and used games, u, for $9. The store earned $7500 in revenue last month. The store sold 4 times as many used games as new games. Write a system of equations that represents this scenario.

Answer 1

u = 4n

19n+9u = 7500

Answer 2

Let's define the following variables:

Let n be the number of new games sold.
Let u be the number of used games sold.

According to the given information, we can form the following equations:

Equation 1: The revenue from new games (19 dollars per game) plus the revenue from used games (9 dollars per game) should equal the total revenue of $7500.
19n + 9u = 7500 (equation 1)

Equation 2: The number of used games sold should be four times the number of new games sold.
u = 4n (equation 2)

So, the system of equations representing this scenario is:
19n + 9u = 7500
u = 4n

Answer 3

Let's denote the number of new games sold as 'x' and the number of used games sold as 'y'.

According to the given information, ABC Game store sells new games, n, for $19, so the revenue generated from the sale of new games would be 19x dollars.

Similarly, ABC Game store sells used games, u, for $9, so the revenue generated from the sale of used games would be 9y dollars.

Now, we know that the total revenue earned by the store last month was $7500. Therefore, we can set up the first equation:

19x + 9y = 7500

Additionally, we are told that the store sold 4 times as many used games as new games, which can be expressed as:

y = 4x

This forms the second equation.

So the system of equations representing this scenario is:

19x + 9y = 7500
y = 4x