Darren bought 3 large popcorn buckets and 2 small drinks for $21. Steve bought 2 large popcorn buckets and 4 small drinks for $22. What is the cost of one large popcorn bucket and one small drink?

Answer 1

Here's yet another system of equations question. They all work pretty much in the same manner!

P = no. popcorn buckets; D = no. drinks.

Darren's cost is 3P + 2D = 21

Steve's cost is 2P + 4D = 22

Now need to decide to use substitution or elimination (or graph) method to solve.

I suggest elimination because 4 is a multiple of 2 (drink terms).

-2(3P + 2D = 21) becomes -6P - 4D = -42 for Darren

Steve is still 2P + 4D = 22

Adding: -4P = -20, so P = -20/-4 = $5

Substituting in the 1st original equation; 3(5) + 2D = 21 → 2D = 6 → D = $3

Let's see if that checks in the 2nd equation (Steve): 2(5) + 4(3) = 10 + 12 = $22 (OK)