$13$ . Liz has a recipe that uses $1 \frac{1}{3}$ cups of sugar and $2 \frac{1}{4}$ cups of flour to make $18$ muffins. She has a total of $9$ cups of flour. Liz wants to use all of her flour to make as many muffins as possible using this recipe. $\newline$ A. Exactly how many cups of sugar will Liz use if she uses all $9$ cups of flour? $\newline$ B. Exactly how many muffins will Liz make if she uses all $9$ cups of flour?

Full solution

13

. Liz has a recipe that uses

1 \frac{1}{3}

cups of sugar and

2 \frac{1}{4}

cups of flour to make

18

muffins. She has a total of

9

cups of flour. Liz wants to use all of her flour to make as many muffins as possible using this recipe.

\newline

A. Exactly how many cups of sugar will Liz use if she uses all

9

cups of flour?

\newline

B. Exactly how many muffins will Liz make if she uses all

9

cups of flour?

Convert to Improper Fraction: Liz's recipe uses $2\left(\frac{1}{4}\right)$ cups of flour for $18$ muffins. Convert mixed number to improper fraction: $2\left(\frac{1}{4}\right) = \frac{9}{4}$ cups of flour.
Calculate Batches of Muffins: Calculate how many batches of muffins Liz can make with $9$ cups of flour. Divide total flour by flour per batch: $9 \div (9/4) = 9 \times (4/9) = 4$ batches.
Convert to Improper Fraction: Liz's recipe uses $1\left(\frac{1}{3}\right)$ cups of sugar for $18$ muffins. Convert mixed number to improper fraction: $1\left(\frac{1}{3}\right) = \frac{4}{3}$ cups of sugar.
Calculate Total Sugar: Calculate total cups of sugar needed for $4$ batches. Multiply sugar per batch by number of batches: $(\frac{4}{3}) \times 4 = \frac{16}{3}$ cups of sugar.
Calculate Total Muffins: Calculate the total number of muffins Liz will make with $4$ batches. Multiply number of muffins per batch by number of batches: $18 \times 4 = 72$ muffins.