How many children does Brenda's family actually have? (II)

Algebra Level 4

Mr and Mrs Tan have a few children with one daughter named Brenda and the rest all sons. 3 years ago, the sum of Mr and Mrs Tan's children was $\frac{3}{5}$ the sum of their ages. This year, the ratio is $\frac{2}{3}$ . 9 years later, the ratio becomes $\frac{5}{6}$ . How many children do the Tans have?

3 Not enough information to determine 4 5

1 solution

Noel Lo
Jun 17, 2015

Let the sum of Mr and Mrs Tan's age be $x$ while that of the $n$ children's ages be $y$ . where $n$ is an integer to be determined.

Evidently, $y = \frac{2}{3} x$

3 years ago, the sum of Mr and Mrs Tan's ages would be $x - 3(2) = x-6$ while that of the $n$ children's ages would be $y - 3n$ .

So $y-3n = \frac{3}{5} (x-6)$

$\frac{2}{3} x - 3n = \frac{3}{5} x - \frac{18}{5}$

Multiplying both sides by 15, we get:

$10x - 45n = 9x - 54$

$x = 45n - 54$

Similarly, 9 years later, the sum of the parents' ages is $x+9(2) = x+18$ while that of the $n$ children would be $y+9n$

So $y+9n = \frac{5}{6} (x+18)$

$\frac{2}{3} x + 9n = \frac{5}{6} x + 15$

Multiplying both sides by 6, we have:

$4x + 54n = 5x + 90$

$x = 54n - 90$

Comparing the two equations with $x$ as the subject,

$45n - 54 = 54n -90$

$9n = 36$

$n = \boxed{4}$

I couldn't figure out what the question was even asking; "the sum of Mr. and Mrs. Tan's children was 3/5 the sum of their ages" does not seem to imply that you are asking about the ratio of the sums of the children's ages to the parents' ages. I thought it was asking for the ratio of the number of children to their collective ages, but that would not correspond to the ratios approaching 1 as time went on so I just chose "not enough info".

Tristan Goodman - 3 months, 3 weeks ago

How many children does Brenda's family actually have? (II)

1 solution

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