Question 1167436: Shirley is combining two nut mixtures to create a new mixture. Both mixes are a combination of peanuts and almonds. The first mixture is 40% almonds and the second is 25% almonds. How much of each mixture should Shirley combine to make 6 kg of a mixture of 33% almonds?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
First, here is a standard setup for solving the problem using algebra.
She wants a total of 6 kg; so let the numbers of kg of the two nut mixtures be x and 6-x.
Then write and solve the equation that says x kg of the first mixture, which is 40% almonds, plus (6-x) kg of the second mixture, which is 25% almonds, yields 6 kg of a mixture that is 33% almonds:
Solve using basic algebra.
If a formal algebraic solution is not required (or if you want to get to the answer as quickly as possible), you can use this method:
(1) Picture the three percentages on a number line: 25, 33, and 40.
(2) Determine with easy calculations that 33 is 8/15 of the way from 25 to 40. (From 25 to 40 is a difference of 15; from 25 to 33 is a difference of 8; 33 is 8/15 of the way from 25 to 40.)
(3) That means 8/15 of the mixture needs to be the mixture that is 40% almonds.
ANSWER: 8/15 of the total 6 kg, or 3.2 kg, of the mixture with 40% almonds; the other 2.8 kg of the mixture with 25% almonds.
CHECK:
.40(3.2)+.25(2.8) = 12.8+7 = 19.8
.33(6) = 19.8
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