A disaster response team has a stockpile of 93 \frac{3}{4} pounds of water purification po… — Armed Services Vocational Aptitude Battery (ASVAB)

A disaster response team has a stockpile of $93 \frac{3}{4}$ pounds of water purification powder. They must first reserve $11 \frac{1}{4}$ pounds of the powder for the main field hospital. The team then distributes the remaining powder evenly into smaller distribution kits. If each kit requires exactly $3 \frac{3}{4}$ pounds of powder, how many complete distribution kits can they fill?

A
25
B
27
22Cevap
D
28

Cevap

The team can fill 22 complete distribution kits.

The correct answer is 22 because the problem requires two steps. First, find the amount of powder available for the kits by subtracting the reserved amount from the total stockpile:

93 \frac{3}{4} - 11 \frac{1}{4} = 82 \frac{2}{4} = 82 \frac{1}{2}

pounds. Second, determine how many kits can be filled by dividing the remaining powder by the amount required per kit:

82 \frac{1}{2} \div 3 \frac{3}{4}

. Convert to improper fractions to divide:

\frac{165}{2} \div \frac{15}{4}

. Multiply by the reciprocal of the divisor:

\frac{165}{2} \times \frac{4}{15}

. Cross-simplify and multiply to get

\frac{11}{1} \times \frac{2}{1} = 22

complete kits.

Adım Adım Çözüm

Subtract the reserved powder from the total stockpile to find the remaining powder available for kits.

93 \frac{3}{4} - 11 \frac{1}{4} = 82 \frac{2}{4} = 82 \frac{1}{2}

pounds

The

11 \frac{1}{4}

pounds are set aside, so they cannot be used to fill the distribution kits.

Divide the remaining powder by the amount of powder required for a single kit.

82 \frac{1}{2} \div 3 \frac{3}{4} = \frac{165}{2} \div \frac{15}{4} = \frac{165}{2} \times \frac{4}{15} = 22

kits

Dividing the total available amount by the size of one batch determines how many complete batches can be formed.

Anahtar Kavram

Solving multi-step word problems involving fraction subtraction and division.

Soru

Cevap

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