Full solution

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} \mathrm{c}

, how many loaves of bread can the baker make with a

10 \mathrm{lb}

-bag of flour?

Calculate Flour Cups: Determine how many cups of flour are in a $10$ lb-bag. We know that $1$ pound of flour is equivalent to $3\left(\frac{1}{3}\right)$ cups. Therefore, we need to multiply the number of pounds by the number of cups per pound to find the total number of cups in a $10$ lb-bag. Calculation: $10 \, \text{lb} \times 3\left(\frac{1}{3}\right) \, \text{c/lb}$
Convert to Improper Fraction: Convert the mixed number to an improper fraction to simplify the multiplication. $\newline$ $3\left(\frac{1}{3}\right)$ cups is the same as $\frac{10}{3}$ cups because $3 \times 3 + 1 = 10$ . $\newline$ Calculation: $10 \, \text{lb} \times \left(\frac{10}{3}\right) \, \text{c/lb}$
Multiply for Total Cups: Multiply the number of pounds by the number of cups per pound to find the total number of cups. $\newline$ Calculation: $10 \, \text{lb} \times \left(\frac{10}{3}\right) \, \text{c/lb} = \frac{100}{3} \, \text{c}$
Determine Loaves of Bread: Determine how many loaves of bread can be made with the total number of cups. $\newline$ We know that $3$ cups of flour are needed for $2$ loaves of bread. Therefore, we need to divide the total number of cups by the number of cups needed for $2$ loaves to find the total number of loaves. $\newline$ Calculation: $(100/3) \, \text{c} \div 3 \, \text{c}/2 \, \text{loaves}$
Simplify Division: Simplify the division by multiplying by the reciprocal of the divisor. $\newline$ Calculation: $(\frac{100}{3} c) \times (\frac{2 \text{ loaves}}{3 c}) = \frac{200}{9} \text{ loaves}$
Convert to Mixed Number: Convert the improper fraction to a mixed number to find the number of whole loaves. $\newline$ Calculation: $\frac{200}{9}$ loaves = $22$ loaves with a remainder, which means the baker can make $22$ whole loaves of bread.