Question #e9cbb

1 Answer
Jan 4, 2018

Small container = 60 and large container = 150

Explanation:

Suppose x containers of small popcorn and y containers of large popcorn were sold.

It's given that the total containers sold were 210

which means x+y = 210 .......(1)

Its also given that the total sale cost was $232.50

Which means 0.75xxx + 1.25xxy = 232.50#.....(2)

Now, using equations (1) and (2) find x and y

Use the method of elimination for any one unknown term, either x or y to solve the equations.

However, we can see that neither x or y terms are equal in any of the equations

To make one of the unknown terms equal - say for example, we try to make x terms equal. For that multiply, equation (1) by the coefficient of x which is 0.75 in equation (2)

On, multiplication by 0.75, equation (1) will look like:

0.75xxx+0.75xxy = 0.75xx210
or, 0.75x+0.75y =157.5..............(3)
Now, we can see that the x terms are equal in both equation (2) and equation (3)

Therefore, subtract equation (2) from equation (3)

cancel0.75x+0.75y =157.5
-
cancel0.75x + 1.25y = 232.50
------------------
or, cancel-0.5y = cancel-75

or, 0.5y=75
or y = 75/0.5 = 150

Now put the value of y in equation (1) and we can get x.

It would be, x+150 = 210

or x = 210-150 = 60