Question 235258: You are ordering softballs for 2 leagues. Pony league uses a ball that costs $2.75, junior league uses a ball that costs $3.25. Total balls bought is 80 for $245. How many for each league were bought?
Answer by MathPro(14)   (Show Source):
You can put this solution on YOUR website! Good evening,
Your problem:
You are ordering softballs for 2 leagues. Pony league uses a ball that costs $2.75, junior league uses a ball that costs $3.25. Total balls bought is 80 for $245. How many for each league were bought?
Call the number of balls that the pony league gets P and the number of balls that the junior league gets J. We are told that a total of 80 balls was bought. So this means that
(1) P+J=80
To digress, if you buy two items at $1.00 each the total cost is 2 x $1.00 = $2.00. Lets calculate the amount of money spent on each team. The price per ball is $2.75 for the ponies, so the total amount of money spent on this team is P x $2.75. The price per ball for the juniors is $3.25 so the total amount of money spent on this team is J x $3.25.
The total amount spent on both teams is the sum of the amount of money spent on each team:
Total amount= P x $2.75 + J x $3.25. We are given the total amount of money spent on both teams in the problem, $245, so we get
(2) 2.75P + 3.25J =245
Now we have two equations with two unknowns. Let’s solve these by substitution:
From equation (1) we get: P = 80 –J
Substitute for P in equation (2) : 2.75(80 –J) +J3.25 = 245
Simplify and solve: 220 +0.5J = 245, 0.5J = 25, J = 50
Substitute for J in equation (1) to get P + 50 = 80, P=30
Check the result by substituting for P and J in equation (2):
2.75(30) + 3.25(50)=245
The left-hand-side is equal to the right-hand-side, so the answer is correct.
Good Luck!
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