Question

You are ordering softballs for two softball leagues. The Pony Leagues uses an 11-inch softball prices at $2.75. The Junior League used a 12-inch softball prices at $3.25. The bill smeared in the rain, but you know the total was 80 softballs for $245. How many of each size did you order?

Answer 1

I have ordered 30 softballs of 11-inch and 50 soft balls of 12-inch.

Explanation:

Let the number of 11-inch softball be 'x'.

Let the number of 12-inch softball be 'y'.

Given:

Total number of soft balls = 80

Now we know that.

Total number of soft balls is equal to sum of the number of 11-inch softball and the number of 12-inch softball.

framing in equation form we get;

`x+y=80 \ \ \ \ equation \ 1`

Also Given:

Price of 11- inch softball = $2.75

Price of 12-inch softball = $3.25

Total Bill = $245

Now we know that;

Total bill of soft balls is equal to sum of Price of 11- inch softball multiplied by the number of 11-inch softball and Price of 12- inch softball the number of 12-inch softball.

framing in equation form we get;

`2.75x+3.25y = 245 \ \ \ \ equation \ 2`

Now Multiplying equation 1 by 3.25 we get;

`3.25(x+y)=80* 3.25\\\\3.25x-3.25y = 260 \ \ \ \ equation \ 3`

Now Subtracting equation 2 from equation 3 we get;

`(3.25x+3.25y)-(2.75x+3.25y)=260-245\\\\3.25x+3.25y-2.75x-3.25y = 15\\\\0.5x = 15`

Dividing both side by 0.5 we get;

`(0.5x)/(0.5)= (15)/(0.5)\\\\x= 30`

Now Substituting the value of 'x' in equation 1 we get;

`x+y=80\\\\30+y=80\\\\y =80-30 =50`

Hence I have ordered 30 softballs of 11-inch and 50 soft balls of 12-inch.