SOLUTION: To create a chocolate blend, chocolate in two concentrations, 56% cocoa and 28% cocoa, are combined together. If 9 ounces of the 56% chocolate is used, how many ounces of the 28% c

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Question 1016083: To create a chocolate blend, chocolate in two concentrations, 56% cocoa and 28% cocoa, are combined together. If 9 ounces of the 56% chocolate is used, how many ounces of the 28% chocolate must be used to obtain a 40% chocolate blend?
If the answer is not an integer, enter it as an exact decimal.
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
F=amount of 56%; T=amount of 28%
.
0.56F+0.28T=0.40(T+F)
0.56(9oz)+0.28T=0.40(T+9oz)
5.04oz+0.28T=0.40T+3.6oz
1.44+0.28T=0.40T
1.44=0.12T
12=T
.
ANSWER: 12 ounces of 28% cocoa should be used.
.
CHECK:
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0.56F+0.28T=0.40(T+F)
0.56(9oz)+0.28(12oz)=0.40(12oz+9oz)
5.04oz+3.36oz=0.40(21oz)
8.4oz=8.4oz
.





Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One material quantity is known and the other is unknown.

Let x be the ounces of the 28% chocolate.

chocolate%2Fmixture=40percent

%289%2A56%2B28x%29%2F%28x%2B9%29=40

STEPS
56%2A9%2B28x=40%28x%2B9%29
56%2A9%2B28x=40x%2B360
40x-28x=56%2A9-360
12x=56%2A9-360
x=%2856%2A9-120%2A3%29%2F12
x=%287%2A8%2A3%2A3-120%2A3%29%2F12
x=14%2A3-30
highlight%28x=12%29


See also the lesson, http://www.algebra.com/my/Two-Part-Mixture-with-one-material-quantity-unknown.lesson?content_action=show_dev