Suppose xx containers of small popcorn and yy containers of large popcorn were sold.
It's given that the total containers sold were 210210
which means x+yx+y = 210210 .......(1)
Its also given that the total sale cost was $232.50$232.50
Which means 0.75xxx + 1.25xxy = 0.75×x+1.25×y=232.50#.....(2)
Now, using equations (1) and (2) find xx and yy
Use the method of elimination for any one unknown term, either xx or yy to solve the equations.
However, we can see that neither xx or yy terms are equal in any of the equations
To make one of the unknown terms equal - say for example, we try to make xx terms equal. For that multiply, equation (1) by the coefficient of xx which is 0.750.75 in equation (2)
On, multiplication by 0.750.75, equation (1) will look like:
0.75xxx+0.75xxy = 0.75xx2100.75×x+0.75×y=0.75×210
or, 0.75x+0.75y =157.50.75x+0.75y=157.5..............(3)
Now, we can see that the xx terms are equal in both equation (2) and equation (3)
Therefore, subtract equation (2) from equation (3)
cancel0.75x+0.75y =157.5
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cancel0.75x + 1.25y = 232.50
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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
