During a one-month promotional campaign, Fran's Flix gave either a free DVD rental or a 12-serving box of microwave popcorn to new members. It cost the store $1 for each free rental and $2 for each box of popcorn. In all, 53 new members were signed up and the store's cost for the incentives was $94. How many of each incentive were given away?

If all of the new members had received free rentals, the cost would have been $53. The cost was actually ($94 -53) = $41 more than that. The additional cost of a box of popcorn is $1, so there must have been 41 boxes of popcorn in the mix of give-aways.

41 boxes of popcorn and 12 free DVD rentals were given away.

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Check

Cost of give-aways was $2×41 +$1×12 = $94, as required.

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If you like to write equations, you can let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...

2p +(53 -p) = 94

p = 94 -53 = 41 . . . . . . . boxes of popcorn

(53 -p) = 53 -41 = 12 . . . DVD rentals

Hopefully, you can see the resemblance to the "word solution" above.