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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?



Answer :

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

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

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

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

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

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

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