Alex is making a nut mixture to sell at the local farmer's market. he mixes 2 pounds of cashews with a nut mixture that is 40% cashews. the resulting mixture is 52% cashews. how many pounds of nut mixture does alex make?

mr. martinez mixes a 90% sugar cinnamon flavored solution with a 75% sugar cherry flavored solution to make 12 gallons of a new product. the new product is 85% sugar. how much of the cherry flavored solution did he use?

mr.acosta works in the lab at a pharmaceutical company. he needs 26 liters of a 36% acid solution to test a new product. his supplier only ships a 42% and a 29% solution. how much of the 42% solution will mr.acosta need to use?

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Question:
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?

We would use the relation c1v1+c2v2=cv
where
v=26 L
c=36%
c1=42%
c2=29%
v1=x
v2=v-x=26-x L

Applying relationship:
42%*x + 29%*(26-x) = 36%*26
Expand
13x+754=936
13x=936-754=182
x=182/13=14 L

Mr. Acosta will need 14 L of 42% solution, and 12 L of 29% solution to make 26 L of 36% solution.

There is a simple diagram that can help make short work of mixture problems. Instances of it are attached.

1. The percentages of cashews available are 100% and 40%. We want to mix these to make 52%. We know that we have used 2 lbs of 100%, and we want to find how much 40% we need.

The first diagram shows the ratio of 40% to 100% will be 48:12. Dividing both terms of this ratio by 6, we get 8:2. This means we will use 8 lbs of 40% cashews with the 2 lbs of 100% cashews, for a total of 10 lbs of mix.

2. The second diagram tells us that 5 out of 15 or 1/3 of the mixture will be cherry-flavored. Of the 12 gallons total, 4 gallons will be cherry-flavored solution.

3. The third diagram shows that 7 of 13 liters will be 42% solution, so to make twice as much mixture, 14 L of 42% solution are needed.

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In each diagram, the right-side numbers are the differences between the middle number and the left-side number.

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over

10

. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

8

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