Systems Word Problem

by Dejoun
(Chicago, IL ,U.S.A)

A baseball team has games on Wednesday and Sunday. The two games together earn 5070.50 for the team. Wednesday's game generates 1095.50 less than Sunday's game.How much money was taken in at each game?

How much money did Wednesday game generate?

How much money did Sunday's game generate?

__________________________________________________'s Response

This problem represents a system of equations word problem. We will need to write two equations and then solve the system of equations.

Let's first define our variables:

Let W = Wednesday night's income
Let S = Sunday night's income

Since we know that the two games together produced $5070.50, we can write the first equation as:

W+S = 5070.50

We also know that Wednesdays game produced 1095.50 less than Sunday's game, so...

W = S-1095.50

To summarize, here are the two equations:
W+S = 5070.50
W = S-1095.50

Now we must solve the system of equations.

Since one of the variables is solved, I will use the substitution method. I will substitute
W = S-1095.50 into the first equation.

W+S = 5070.50
S-1095.50 +S = 5070.50
2s - 1095.50 = 5070.50 - combine like terms

Now add 1095.50 to both sides:
2s - 1095.50 +1095.50 = 5070.50 + 1095.50
2s = 6166

Divide both sides by 2:
2s/2 = 6166/2
s = 3083

Now we know Sunday's game produced 3083.00

Substitute to find Wednesday's game earnings.
W = s-1095.50
W = 3083.00-1095.50
W = 1987.50

Sunday's game earnings were $3083.00
Wednesday's game earnings were $1987.50

To check your answer, add the two amounts to verify that they equal $5070.50

3083+1987.50 = 5070.50

I hope this helps!


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