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.