Answered

The ratio of the number of adults to the number of children on a
ferry is 8: 3. When 10 adults get down from the ferry, the ratio of
the number of adults to the number of children becomes 2: 1. How
many children are there on the ferry?

Verified Answer :

GinnyAnswer

Let's solve the problem step-by-step.

1. Initial Ratios and Variables Setup:
- Let \(\( A \)\) be the number of adults and \(\( C \)\) be the number of children on the ferry initially.
- The ratio of adults to children is given by:
\(\[ \frac{A}{C} = \frac{8}{3} \]\)
- We can express \(\( A \)\) in terms of \(\( C \)\):
\(\[ A = \frac{8}{3}C \]\)

2. Condition After Adults Get Down:
- When 10 adults get down, the number of adults becomes \(\( A - 10 \)\).
- The new ratio of adults to children is given as \(\( 2:1 \)\):
\(\[ \frac{A - 10}{C} = \frac{2}{1} \]\)
- This gives us the equation:
\(\[ A - 10 = 2C \]\)

3. Substitute \(\( A \)\) from the First Equation:
- We already have \(\( A = \frac{8}{3}C \)\).
- Substitute \(\( A \)\) in the second equation:
\(\[ \frac{8}{3}C - 10 = 2C \]\)

4. Solve for \(\( C \)\):
- Clear the fraction by multiplying all terms by 3:
\(\[ 8C - 30 = 6C \]\)
- Simplify the equation:
\(\[ 8C - 6C = 30 \]\)
\(\[ 2C = 30 \]\)
\(\[ C = 15 \]\)

Hence, the number of children on the ferry is 15.

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