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?

Let the count of full batches using #3/4# cup be #B#

#color(blue)("Information from question")#

Sugar#->4 lb ->454 " teaspoons" ->$3.49#

1 full cooking batch uses #3/4# cup of sugar
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#color(brown)("Using the units of measurements to indicate the method of calculation")#

#color(blue)("Method ")#
batches cooked = total teaspoons available #-:# teaspoons in #3/4# cup

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

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#color(blue)("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

#->237-:5 = 237/5 ("teaspoons")/("cup")#
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#color(blue)("Step 2: Completing the calculation by substituting values")#

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

#"full batches cooked" =B=454-:(3/4xx237/5)#

#B=454-:711/20#

#B= 12 548/711 = 9080/711~~12.77" "# to 2 decimal places

All the sugar used #-> 12.77" batches"#

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