Question

Pooja is making punch for a winter party in a punch bowl that can hold at most $9$ quarts. She wants to get as much vitamin C in her punch as possible, so she is suing only orange juice and grape juice. She has $6$ quarts of orange juice, which has $2$ grams of vitamin C per quart and $7$ quarts of grape juice, which has $1$ gram of vitamin C per quart. If there are $4$ cups in a quart, what is the maximum amount of vitamin C, in grams, that Pooja can have in one cup of her punch?

• A. $\frac{5}{12}$
• B. $\frac{3}{8}$
• C. $\frac{4}{9}$
• D. $\frac{2}{9}$

Answer 1

Answer: (A)

$\frac{5}{12}$

$\because$ Pooja wanted to get as much vitamin $C$ in her punch as possible.

$\therefore$ She used $6$ quarts of orange juice and $3$ quart of grape juice.

$\therefore$ Grams of vitamin $C$ in orange juice$=6\times 2=12$

$\therefore$ Grams of vitamin $C$ in grape juice$=3\times 1=3$

$\therefore$ Total grams of vitamin $C$ in $9$ quarts$=12+3=15$

$\therefore$ Total grams of vitamin $C$ in $1$ quarts$=\frac{15}{9}=\frac{5}{3}$

$\because 4$ cups are there in $1$ quart

$\therefore 1$ cup contains $\frac{1}{4}$ quart.

$\therefore$ Total grams of vitamin $C$ in $\frac{1}{4}$ quarts= $\frac{5}{3}\times 14=\frac{5}{12}$