document.write( "Question 61622: The local yogurtbar features a banana treat made up of 2lb of bananas, 3lb of topping, and 4lb of frozen yogurt. The cost of the banana treat is $19.00. One pound of topping cost $1 less than one pound of frozen yogurt, which costs as much as 1/2 pound of topping and 4 pound of bananas. How much does one pound of each ingredient cost? \n" ); document.write( "
Algebra.Com's Answer #42472 by ankor@dixie-net.com(22740)\"\" \"About 
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The local yogurt bar features a banana treat made up of 2 lb of bananas, 3 lb of topping, and 4 lb of frozen yogurt. The cost of the banana treat is $19.00. One pound of topping cost $1 less than one pound of frozen yogurt, which costs as much as 1/2 pound of topping and 4 pound of bananas. How much does one pound of each ingredient cost?
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\n" ); document.write( "Let b = banana cost; t = topping cost, y = yogurt cost
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\n" ); document.write( "\"One pound of topping cost $1 less than one pound of frozen yogurt\"
\n" ); document.write( " t = y - 1
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\n" ); document.write( "\"yogurt costs as much as 1/2 pound of topping and 4 pound of bananas\"
\n" ); document.write( ".5t + 4b = y
\n" ); document.write( "Try to arrange equation to get it in terms of y also:
\n" ); document.write( "4b = y - .5t
\n" ); document.write( "Subtsitute (y-1) for t (from the topping equation)
\n" ); document.write( "4b = y - .5(y-1)
\n" ); document.write( "4b = y - .5y + .5
\n" ); document.write( "4b = .5y + .5
\n" ); document.write( "b = (.5/4)y + .5/4
\n" ); document.write( "b = .125y + .125
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\n" ); document.write( "The mixture consists of 2 lb of bananas, 3 lb topping, and 4 lb of yogurt and costs 19.00
\n" ); document.write( "2b + 3t + 4y = 19
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\n" ); document.write( "Substitute (y-1) for t and (.125y + .125) for b, solve for y:
\n" ); document.write( "2(.125y + .125 + 3(y-1) + 4y = 19
\n" ); document.write( ".25y + .25 + 3y - 3 + 4y = 19
\n" ); document.write( ".25y + 3y + 4y = 19 - .25 + 3
\n" ); document.write( "7.25y = 21.75
\n" ); document.write( "y = 21.75/7.25
\n" ); document.write( "y = $3 a pound for yogurt
\n" ); document.write( ":
\n" ); document.write( "Find topping price:
\n" ); document.write( "t = 3 - 1
\n" ); document.write( "t = $2 a pound for topping
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\n" ); document.write( "Find banana price:
\n" ); document.write( "b = .125(3) + .125
\n" ); document.write( "b = .375 + .125
\n" ); document.write( "b = $.50 a pound for bananas
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\n" ); document.write( "Check our solutions: .5(2) + 3(2) + 4(3) = 19.00
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\n" ); document.write( "could you follow this OK?\r
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