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...

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
pohnpei397 eNotes educator| Certified Educator

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.

 

neela | Student

You can get it . As you stiil have the price of both types: pony and junior ball .  You can do this single variable type also. You can do this by a lay man's guess also:

If all the ball's were of the type $2.25, then you have $80*2.25  = 180. So this cannot be as the the value of the total 80 ball's is $210.So you require another $30 worth replacement  with $2.75 rated balls inplace of $2.25 ball's.

Replace a ball of price $2.25 by a 2.75 ball  raises the value by $(2.75-2.25) = $0.50. So we require  30/0.5 = 60 replacements. So  It is now 80-60 = 20 number of ball's of price $2.25 and  60 number of balls of price $2.75 balls .

Tally: Value of 20 balls of price $2.25 = $45

Value of 60 balls of price $2.75 = $165

Total value of 80 balls = $(45+165) = $210