# SOLUTION: The local yogurt bar 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

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: The local yogurt bar 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      Log On

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 Click here to see ALL problems on Matrices-and-determiminant Question 61637: The local yogurt bar 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 costs \$1 less than one pound of frozen yogurt, which costs as much as 1/2 pound of topping and 4 pounds of bananas. How much does one pound of each ingredient cost?Answer by ptaylor(2048)   (Show Source): You can put this solution on YOUR website!Let x=cost of bananas (\$) Let y=cost of topping (\$) Let z=cost of frozen yogurt(\$) Now we know that the cost of 2 lb of bananas (2x) plus the cost of 3 lb of topping (3y) plus the cost of 4 lb of frozen yogurt (4z)equals \$19.00. This gives us one of the three equations that we need in order to solve this problem. (1) 2x+3y+4z=19 We are told that one lb of topping (y) costs \$1 less that one lb of frozen yogurt (z). This gives us our second equation: y=z-1 or (2) y-z=-1 We are also told that the cost of frozen yogurt (z) is the same as the cost of 1/2 lb of topping (1/2y) plus 4 lb of bananas (4x). Now we have our third equation: z=(1/2)y+4x or (3) 8x+y-2z=0 Putting our three equations together, we have: (1) 2x+3y+4z=19 (2) y-z=-1 (3) 8x+y-2z=0 I will solve these by simply manipulating the equations and you can solve them by the use of matrices. First, solve for z in (2) and substitute into (1) and (3) and we now have: (1a) 2x+3y+4(y+1)=19 and 2x+7y=15 (3a) 8x+y-2(y+1)=0 and 8x-y=2 Solve for y in (3a) and substitute into (1a) and we get: (1b) 2x+7(8x-2)=15 simplifying we get: 58x=29 x=\$.50 cost of bananas From (3a) 8x-y=2 or (8)(.50)-y=2 y=\$2.00 cost of topping From (2) above we have y-z=-1 or z=y+1 Substuting \$2.00 for y, we have: z=\$3.00 cost of frozen yogurt Hope this helps-----ptaylor