A school district requires a chaperone-to-student ratio of 3:5 for all field trips. If the… — ACT

A school district requires a chaperone-to-student ratio of $3:5$ for all field trips. If there are exactly $15$ chaperones registered for an upcoming field trip, what is the maximum number of students who can attend?

A
$9$
B
$17$
C
$24$
$25$ Answer
E
$40$

Answer

The maximum number of students who can attend is

25

The correct answer is

25

. To maintain the required ratio of

3

chaperones to

5

students, we set up the proportion

\frac{3}{5} = \frac{15}{x}

, where

x

is the number of students. Cross-multiplying gives

3x = 75

, and dividing by

3

gives

x = 25

Step-by-Step Solution

Set up the proportion using the given chaperone-to-student ratio.

\frac{\text{Chaperones}}{\text{Students}} = \frac{3}{5} = \frac{15}{x}

, where

x

represents the maximum number of students.

Establishing a direct proportion allows us to find the unknown quantity while maintaining the required ratio.

Solve for the unknown variable

x

by cross-multiplying.

3 \times x = 5 \times 15 \implies 3x = 75

Cross-multiplication is a standard algebraic method to solve proportions.

Divide both sides of the equation by

3

to isolate

x

x = 25

This yields the final value of students who can attend.

Key Concept

Solving direct proportions from part-to-part ratios

Estimated Time:45s

Question

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Step-by-Step Solution

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