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# Algebra

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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 75% magical syrup by volume (and the rest is just water), and blue potion, which is 15% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)

(a) Find the amount of red potion (in mL) that must be added to 200 mL of blue potion in order to produce potion that is 25% magical syrup by volume.

(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 400 mL of a potion that is 30% magical syrup by volume.

(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 35% magical syrup by voume?

Dec 25, 2022

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(a)

Let the amount of 75% red potion needed==R

0.75R  +  0.15(200) ==0.25[R + 200], solve for R

R ==40 mL of red potion needed

(b)

0.75R  +  0.15[400 - R] ==0.30[400], solve for R

R ==100 mL of red potion needed

400 - 100 ==300 mL of blue potion needed.

(c)

Yes, there is. Example:

0.75[40]  +  0.15[80] ==0.35[40 + 80]

30         +     12         == 42

42  ==  42

Dec 26, 2022