Question

The town recreation department ordered a total of 100 baseballs and bats for the summer.Baseballs cost $4.50 each and bats cost $20 each. The total purchase was $822. How many of each item was ordered.

Answer 1

The town recreation department ordered 66 baseballs and 24 bats.

Explanation:

Let the number of baseball be 'x'.

Also Let the number of bats be 'y'.

Given:

Total items bought = 100

Now we can say that;

Total items bought is equal to sum of number of baseball and number of bats.

Framing in equation form we get;

`x+y =100 \ \ \ \ equation \ 1`

Also Given:

Cost of each baseball = $4.50

Cost of each bat = $20

Total purchase = $822

Now we can say that;

Total Purchase is equal to to sum of number of baseball multiplied by Cost of each baseball and number of bats multiplied by Cost of each bat.

framing in equation form we get;

`4.5x+20y =822 \ \ \ \ equation\ 2`

Multiplying equation 1 by 4.5 we get;

`4.5(x+y) =100*4.5\\\\4.5x+4.5y = 450 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 2 we get;

`(4.5x+20y)-(4.5x+4.5y) = 822-450\\\\4.5x+20y-4.5x-4.5y =372\\\\15.5y = 372`

Dividing both side by 15.5 we get;

`(15.5y)/(15.5)= (372)/(15.5)\\  \\y =24`

Substituting the value of y in equation 1 we get;

`x+y =100\\\\x+24 =100\\\\x =100-24 =66`

Hence the town recreation department ordered 66 baseballs and 24 bats.