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#
