SOLUTION: 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 $
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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?
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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?
:
Let b = banana cost; t = topping cost, y = yogurt cost
:
"One pound of topping cost $1 less than one pound of frozen yogurt"
t = y - 1
:
"yogurt costs as much as 1/2 pound of topping and 4 pound of bananas"
.5t + 4b = y
Try to arrange equation to get it in terms of y also:
4b = y - .5t
Subtsitute (y-1) for t (from the topping equation)
4b = y - .5(y-1)
4b = y - .5y + .5
4b = .5y + .5
b = (.5/4)y + .5/4
b = .125y + .125
:
The mixture consists of 2 lb of bananas, 3 lb topping, and 4 lb of yogurt and costs 19.00
2b + 3t + 4y = 19
:
Substitute (y-1) for t and (.125y + .125) for b, solve for y:
2(.125y + .125 + 3(y-1) + 4y = 19
.25y + .25 + 3y - 3 + 4y = 19
.25y + 3y + 4y = 19 - .25 + 3
7.25y = 21.75
y = 21.75/7.25
y = $3 a pound for yogurt
:
Find topping price:
t = 3 - 1
t = $2 a pound for topping
:
Find banana price:
b = .125(3) + .125
b = .375 + .125
b = $.50 a pound for bananas
:
Check our solutions: .5(2) + 3(2) + 4(3) = 19.00
:
could you follow this OK?
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