I need help on a 2 variable equation. the problem is: There are 2 softball leagues the pony league and the junior league. They need to get some new softballs. The Pony league's softballs cost $2.25 and the Junior league's cost $2.75. Unfortunatley the inventory list saying how many of each league was needed was washed away in the rain, all that is left is the total number of softballs-80 and the total price-$210.How many softball of each league is needed?

Expert Answers

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The answer to this is that you need to buy 60 of the Junior league softballs and 20 of the Pony league softballs.  Here is how to get to this answer:

Let P be the number of Pony league balls and J be the number of Junior league balls.

P + J = 80 because that's how many balls there are.

2.25P + 2.75J = 210 because the number of P balls times their price plus the number of J balls times their price come to $210.

So now you substitute for one of the variables.  You can use the first equation to do this.  You can subtract J from both sides and get P = 80 - J.  Now sub that into the other equation.  That gets you

2.25 (80 - J) + 2.75 J = 210.

180 - 2.25 J + 2.75 J = 210

180 + .5J = 210

.5J + 30

J = 60

If J = 60 and P + J = 80, then P = 20.

You can check that by multiplying those numbers by the prices.  Add what you get together and you end up with 210.

 

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