SOLUTION: write and solve a system of equations to find the cost of a large popcorn and the cost of a small drink. 3 large popcorns buckets 2 small drinks total $21.00 2 large popcorns buc

Question 717335: write and solve a system of equations to find the cost of a large popcorn and the cost of a small drink.
3 large popcorns buckets 2 small drinks total $21.00
2 large popcorns buckets 4 small drinks total $22.00
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Let p = the cost of a popcorn
and d = the cost of a drink

Then "3 large popcorns buckets 2 small drinks total $21.00" translates into:
3p + 2d = 21
and "2 large popcorns buckets 4 small drinks total $22.00" translates into:
2p + 4d = 22

3p + 2d = 21
2p + 4d = 22
Many methods are taught which can be used to solve such a system. The method I'll use is called Linear Combination (aka Elimination or Addition). I'm choosing this method because the first part of this method involves setting up opposite terms in the two equations. And I can see that all I have to do is multiply the first equation by -2 and the y terms will be opposites of each other. This is a fairly easy start. (If you know determinants and Cramer's rule then that is another good method for this problem.)

Multiplying the first equation by -2:
-6p + (-4d) = -42
2p + 4d = 22
Now we add the equations together. The opposite y terms cancel out.
-4p = -20
Dividing by -4:
p = 5

Now we can use this value for p and one of the original equations to find the value for d:
3(5) + 2d = 21
15 + 2d = 21
Subtract 15:
2d = 6
Divide by 2:
d = 3

So the popcorn costs $5 each and the drinks $3 each.
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