SOLUTION: A movie theater sells two different size boxes of popcorn. The large box costs $3 and the small box costs $2. In one day, the theater sold 657 boxes of popcorn for a total of $16

Question 64191: A movie theater sells two different size boxes of popcorn. The large box costs $3 and the small box costs $2. In one day, the theater sold 657 boxes of popcorn for a total of $1612. How many of each size were sold? (Use a four-column table.)
Answer by burkus(4) (Show Source): You can put this solution on YOUR website!
LARGE = 3.00
small = 2.00
657 boxes on day
1612 total on day
Let L be the number of boxes of LARGE
Let s be the number of boxes of small
L + s = 657
L * 3.00 + s * 2.00 = 1612.00
two equations and two unknowns
Let's subsitute for L using s, from the L + s = 657 equation.
L + s = 657
L = 657 - s
and plugin to the second equation, gives
( 657 - s ) * 3.00 + s * 2.00 = 1612.00
1971 - s * 3.00 + s * 2.00 = 1612.00
subtract 1971 from both sides
-s * 3.00 + s * 2.00 = 1612 - 1971
-3 s + 2 s = 1612 - 1971
-1 s = 1612 - 1971
-s = -359
or s = 359.
Plug this new found value for s back into the original equation,
and get L
L + s = 657
L + 359 = 657
L = 657 - 359
L = 298

So, in answer to how many of each boxes were sold on that day,
298 Large and 359 small boxes were sold.

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