A baker uses $3$ cups $(c)$ of flour to bake $2$ loaves of bread. If $1$ pound $(lb)$ of flour is equivalent to $3\frac{1}{3} c ,$ how many loaves of bread can the baker make with a $10$ $lb$ - bag of flour? $\newline$ (Round the answer to the nearest whole number.) $\newline$ $\square$

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Identify quotients of rational numbers: word problems

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Q. A baker uses

3

cups

(c)

of flour to bake

2

loaves of bread. If

1

pound

(lb)

of flour is equivalent to

3\frac{1}{3} c ,

how many loaves of bread can the baker make with a

10

lb

- bag of flour?

\newline

(Round the answer to the nearest whole number.)

\newline

\square

Determine Flour Cups: First, we need to determine how many cups of flour are in a $10 \, \text{lb}$ bag. $\newline$ We know that $1 \, \text{lb}$ of flour is equivalent to $3 \, 1/3$ cups. $\newline$ So, we multiply $10 \, \text{lb}$ by $3 \, 1/3 \, \text{cups}$ to find the total number of cups in a $10 \, \text{lb}$ bag. $\newline$ Calculation: $10 \, \text{lb} \times 3 \, 1/3\text{c} = 10 \, \text{lb} \times (10/3)\text{c}$
Calculate Total Cups: Now, we perform the multiplication to find the total number of cups. $\newline$ Calculation: $10 \times \left(\frac{10}{3}\right) = \frac{100}{3} = 33 \frac{1}{3}$ cups
Find Loaves of Bread: Next, we need to find out how many loaves of bread can be made with $33 \frac{1}{3}$ cups of flour. $\newline$ We know that $3$ cups of flour are needed for $2$ loaves of bread. $\newline$ So, we divide $33 \frac{1}{3}$ cups by $3$ cups to find the number of sets of $2$ loaves we can make. $\newline$ Calculation: $33 \frac{1}{3}c \div 3c = \left(\frac{100}{3}\right)c \div 3c = \left(\frac{100}{3}\right) \div 3 = \frac{100}{9}$
Calculate Sets of Loaves: Now, we calculate the number of sets of $2$ loaves. $\newline$ Calculation: $100/9 \approx 11.11$ $\newline$ This means we can make approximately $11.11$ sets of $2$ loaves of bread.
Calculate Total Loaves: Since each set consists of $2$ loaves, we multiply the number of sets by $2$ to find the total number of loaves. $\newline$ Calculation: $11.11 \times 2 \approx 22.22$ loaves
Round to Nearest Whole: We need to round the number of loaves to the nearest whole number, as the question prompt asks for this. $\newline$ Calculation: $22.22$ loaves rounded to the nearest whole number is $22$ loaves.