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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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\n" ); document.write( "Let last year's price for each item be h, f, c:
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\n" ); document.write( "Write an equation for each statement:
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\n" ); document.write( "\"you could get a hamburger, fries and a cola at Fransisco's Drive-In for $2.90.\"
\n" ); document.write( "h + f + c = 2.90
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\n" ); document.write( "\"the price of a hamburger has increased %10\"
\n" ); document.write( "1.10h; is the price now
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\n" ); document.write( "\"the price of fries has increased %30\"
\n" ); document.write( "1.30f; is the price now
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\n" ); document.write( "\"the price of cola has increased %40,\"
\n" ); document.write( "1.40c; is the price now
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\n" ); document.write( "\"the same meal costs $3.67.\"
\n" ); document.write( "1.1h + 1.3f + 1.4c = 3.67
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\n" ); document.write( "\"If the price of cola is now 13 cents more than that of a hamburger,\"
\n" ); document.write( "1.4c = 1.1h + .13
\n" ); document.write( "rearrange to:
\n" ); document.write( "1.4c - 1.1h = .13
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\n" ); document.write( "Do some elimination to give us two 2 unknown equations:
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\n" ); document.write( "Multiply the last year total equation by 1.4, subtract the new total equation:
\n" ); document.write( "1.4h + 1.4f + 1.4c = 4.06
\n" ); document.write( "1.1h + 1.3f + 1.4c = 3.67
\n" ); document.write( "---------------------------subtraction eliminates c
\n" ); document.write( "0.3h + 0.1f + 0c = .39; (the 1st two unknown equation)
\n" ); document.write( "3h + 1f = 3.9; (multiplied by 10 to get rid of some of the decimals
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\n" ); document.write( "Using the same equation, subtract 1.4c - 1.1h = .13
\n" ); document.write( "+1.4h + 1.4f + 1.4c = 4.06
\n" ); document.write( "-1.1h + 0.0f + 1.4c = 0.13
\n" ); document.write( "---------------------------- subtraction eliminate c again
\n" ); document.write( "2.5h + 1.4f + 0c = 3.93; (the 2nd two unknown equation)
\n" ); document.write( "25h + 14f = 39.3; (multiplied by 10)
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\n" ); document.write( "Multiply the 1st two unknown equation by 14 and subtract the 2nd one
\n" ); document.write( "42h + 14f = 54.6
\n" ); document.write( "25h + 14f = 39.3
\n" ); document.write( "------------------subtraction eliminates f and we can find h!
\n" ); document.write( "17h + 0f = 15.3
\n" ); document.write( "h =
\n" ); document.write( "h = .90 is the price of a hamburger a year ago:
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\n" ); document.write( "1.4c - 1.1h = .13
\n" ); document.write( "Substitute .90 for h
\n" ); document.write( "1.4c - 1.1(.90) = .13
\n" ); document.write( "1.4c - .99 = .13
\n" ); document.write( "1.4c = .13 + .99
\n" ); document.write( "1.4c = 1.12
\n" ); document.write( "c =
\n" ); document.write( "c = .80 is the price of a cola last year
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\n" ); document.write( "Use the last year total equation to find f
\n" ); document.write( ".90 + f + .80 = 2.90
\n" ); document.write( "f = 2.90 - 1.70
\n" ); document.write( "f = 1.20 is the price of fries last year
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\n" ); document.write( "you can check our solutions in the present total equation
\n" ); document.write( "1.1(.90) + 1.3(1.20) + 1.4(.80) = 3.67??
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\n" ); document.write( "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 \n" ); document.write( "