Question 1191329: Two families went to an amusement park together. Family A bought three hotdogs and two pies for $16 and family B spent $22 to get 4 hotdogs and three pies. Find the cost of each hotdog and each pie.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The equations we can form from the given information are
3h+2p=16 the cost of 3 hot dogs and 2 pies is $16
4h+3p=22 the cost of 4 hot dogs and 3 pies is $22
With the two equations in that form, a typical algebraic solution would use elimination. Multiply both equations by some numbers so that the coefficients of one of the variables are opposites; then adding the two resulting equations eliminates that variable. Then the rest of the path to the solution is easy.
In this example, we can multiply the first equation by 3 and the second by -2; that makes the coefficients of p in the two equation 6 and -6.
9h+6p=48
-8h-6p=-44
h=4
Plug that value for h into either original equation to solve for p.
3(4)+2p=16
12+2p=16
2p=4
p=2
ANSWER: hot dogs cost $4 each; pies cost $2 each.
The particular numbers in this example make it easy to solve the problem informally using logical reasoning.
4 hot dogs and 3 pies cost $22
3 hot dogs and 2 pies cost $16
The difference between the two purchases is 1 hot dog and 1 pie, for a cost of $6. Continue subtracting 1 hot dog and 1 pie for $6 until you are left with only 1 hot dog:
3 hot dogs and 2 pies cost $16
2 hot dogs and 1 pie cost $10
1 hot dog and 0 pies cost $4
So each hot dog costs $4; then, since 1 hot dog and 1 pie cost $6, each pie costs $2.
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