Question 151393: Could you please help me with this word problem?
Last year you could get a hamburger, fries and a cola at Fransisco's Drive-In for $2.90. Since the price of a hamburger has increased %10, the price of fries has increased %30 and the price of cola has increased %40, the same meal costs $3.67. If the price of cola is now 13 cents more than that of a hamburger, what was the price of each item last year?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Last year you could get a hamburger, fries and a cola at Fransisco's Drive-In for $2.90. Since the price of a hamburger has increased %10, the price of fries has increased %30 and the price of cola has increased %40, the same meal costs $3.67. If the price of cola is now 13 cents more than that of a hamburger, what was the price of each item last year?
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Let last year's price for each item be h, f, c:
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Write an equation for each statement:
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"you could get a hamburger, fries and a cola at Fransisco's Drive-In for $2.90."
h + f + c = 2.90
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"the price of a hamburger has increased %10"
1.10h; is the price now
;
"the price of fries has increased %30"
1.30f; is the price now
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"the price of cola has increased %40,"
1.40c; is the price now
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"the same meal costs $3.67."
1.1h + 1.3f + 1.4c = 3.67
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"If the price of cola is now 13 cents more than that of a hamburger,"
1.4c = 1.1h + .13
rearrange to:
1.4c - 1.1h = .13
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Do some elimination to give us two 2 unknown equations:
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Multiply the last year total equation by 1.4, subtract the new total equation:
1.4h + 1.4f + 1.4c = 4.06
1.1h + 1.3f + 1.4c = 3.67
---------------------------subtraction eliminates c
0.3h + 0.1f + 0c = .39; (the 1st two unknown equation)
3h + 1f = 3.9; (multiplied by 10 to get rid of some of the decimals
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Using the same equation, subtract 1.4c - 1.1h = .13
+1.4h + 1.4f + 1.4c = 4.06
-1.1h + 0.0f + 1.4c = 0.13
---------------------------- subtraction eliminate c again
2.5h + 1.4f + 0c = 3.93; (the 2nd two unknown equation)
25h + 14f = 39.3; (multiplied by 10)
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Multiply the 1st two unknown equation by 14 and subtract the 2nd one
42h + 14f = 54.6
25h + 14f = 39.3
------------------subtraction eliminates f and we can find h!
17h + 0f = 15.3
h = 
h = .90 is the price of a hamburger a year ago:
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1.4c - 1.1h = .13
Substitute .90 for h
1.4c - 1.1(.90) = .13
1.4c - .99 = .13
1.4c = .13 + .99
1.4c = 1.12
c = 
c = .80 is the price of a cola last year
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Use the last year total equation to find f
.90 + f + .80 = 2.90
f = 2.90 - 1.70
f = 1.20 is the price of fries last year
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you can check our solutions in the present total equation
1.1(.90) + 1.3(1.20) + 1.4(.80) = 3.67??
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I know there are a lot of steps here, try to understand each one and it will make sense. You can email me if you have any questions
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