SOLUTION: At a concession stand, three hot dogs and two hamburgers cost $7.50; two hot dogs and three hamburgers cost $8.75. Find the cost of one hot dog and one hamburger

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: At a concession stand, three hot dogs and two hamburgers cost $7.50; two hot dogs and three hamburgers cost $8.75. Find the cost of one hot dog and one hamburger      Log On


   

Question 957470: At a concession stand, three hot dogs and two hamburgers cost $7.50; two hot dogs and three hamburgers cost $8.75. Find the cost of one hot dog and one hamburger
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost in dollars of 1 hot dog
Let +b+ = the cost in dollars of 1 hamburger
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given:
(1) +3a+%2B+2b+=+7.5+
(2) +2a+%2B+3b+=+8.75+
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Multiply both sides of (1) by +2+
Multiply both sides of (2) by +3+
Subtract (1) from (2)
(2) +6a+%2B+9b+=+26.25+
(1) +-6a+-+4b+=+-15+
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+5b+=+11.25+
+b+=+2.25+
and
(1) +3a+%2B+2%2A2.25+=+7.5+
(1) +3a+=+7.5+-+4.5+
(1) +3a+=+3+
(1) +a+=+1+
1 hot dog costs $1
1 hamburger costs $2.25
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check:
(1) +3%2A1+%2B+2%2A2.25+=+7.5+
(1) +3+%2B+4.5+=+7.5+
(1) +7.5+=+7.5+
and
(2) +2%2A1+%2B+3%2A2.25+=+8.75+
(2) +2+%2B+6.75+=+8.75+
(2) +8.75+=+8.75+
OK