# A 4-pound bag of sugar contains 454 one teaspoon servings and costs $3 49, A batch of muffins uses 3/4 cup of sugar. How many batches can you make if you use all the sugar? What is the cost of sugar for each? ##### 1 Answer Mar 19, 2017 All the sugar used $\to 12.77 \text{ batches}$Cost of sugar for each batch is ~~($3.49)-:12.77~~ $0.273 #### Explanation: Let the count of full batches using $\frac{3}{4}$cup be $B$$\textcolor{b l u e}{\text{Information from question}}$Sugar->4 lb ->454 " teaspoons" ->$3.49

1 full cooking batch uses $\frac{3}{4}$ cup of sugar
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$\textcolor{b r o w n}{\text{Using the units of measurements to indicate the method of calculation}}$

$\textcolor{b l u e}{\text{Method }}$
batches cooked = total teaspoons available $\div$ teaspoons in $\frac{3}{4}$ cup

batches cooked = total teaspoons " -: (3/4" cup"xx ("teaspoons")/("cup"))

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$\textcolor{b l u e}{\text{Step 1: Determine the count of teaspoons in 1 cup.}}$

1 teaspoon = 5 ml

1 cup = 237 ml

teaspoon count per cup is how many lots of 5ml will fit into 237 ml

$\to 237 \div 5 = \frac{237}{5} \left(\text{teaspoons")/("cup}\right)$
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$\textcolor{b l u e}{\text{Step 2: Completing the calculation by substituting values}}$

batches cooked = total teaspoons -: (3/4" cup"xx ("teaspoons")/("cup"))

$\text{full batches cooked} = B = 454 \div \left(\frac{3}{4} \times \frac{237}{5}\right)$

$B = 454 \div \frac{711}{20}$

$B = 12 \frac{548}{711} = \frac{9080}{711} \approx 12.77 \text{ }$ to 2 decimal places

All the sugar used $\to 12.77 \text{ batches}$

Cost of sugar for each batch is ~~($3.49)-:12.77~~$0.273