SOLUTION: Will the equation 2a+3e=58.75 or 4a+5e=102.50 work for this word problem? a-appetizers, e-entrees At a restaurant, the Jones family orders two of the same appetizers, and thr

Question 875598: Will the equation 2a+3e=58.75 or 4a+5e=102.50 work for this word problem?
a-appetizers, e-entrees
At a restaurant, the Jones family orders two of the same appetizers, and three of the same entrees. Their bill (not including tax and/or tip) came to $58.75.
Later, the Williamsons ordered the same appetizers and entrees, just on different quantities. The Williamsons ordered four appetizers and five entrees. Their bill (not including tax and/or tip) came to $102.50.
What was the cost of the appetizer and the entree that the families ordered?
I have tried using 2a+3e=58.75 but I don't know what to do next with my answer.
My work:
2a+3e=58.75
-3e on both sides
2a=58.75-3e
divide by 2 on both sides
a=29.375-3/2e
a=29.375-1.5e
I tried pluging in 'a' into the original equation
2(29.375-1.5e)+3e=58.75
58.75-3e+3e=58.75
58.75=58.75 - which is one and I don't think that's the answer.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
2a + 3e = 58.75
4a + 5e = 102.50
solve first equation for a
2a = 58.75 - 3e
a = (58.75 - 3e) / 2
now substitute for a in the second equation
4(58.75 - 3e) / 2 +5e = 102.50
2(58.75 - 3e) + 5e = 102.50
117.50 - 6e + 5e = 102.50
-e = -15
e = 15.00
now substitute for e in first equation
2a + 45.00 = 58.75
2a = 13.75
a = 6.875
therefore
e = $15.00 and a = $6.875

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