Riley and her children went into a movie theater and she bought $51 worth of bags of popcorn and drinks. Each bag of popcorn costs $5 and each drink costs $6. She bought twice as many drinks as bags of popcorn. Determine the number of bags of popcorn and the number of drinks that Riley bought.

Answer 1

Let the number of bags of popcorn be represented by P and the number of drinks be represented by D.

Given:
5P + 6D = 51 (total cost of bags of popcorn and drinks)
D = 2P (twice as many drinks as bags of popcorn)

Substitute D = 2P into the first equation:
5P + 6(2P) = 51
5P + 12P = 51
17P = 51
P = 3

Now, substitute P = 3 back into D = 2P:
D = 2(3)
D = 6

Riley bought 3 bags of popcorn and 6 drinks.