## Prove it by solving this puzzle!

Earlier this month, more than 200,000 British students took the UK Mathematics Trust (UKMT) Intermediate Mathematical Challenge for 13 to 16 year olds. This is one of the questions from it, and apparently only 15 percent of students answered it correctly. They got to choose from multiple-choice options — 5, 7, 9, 11 or 13 — but no calculators were allowed.

*The Guardian* published a selection of questions from the competition, and only 23 percent of their readers answered this question successfully. The fact that more readers got it right than students may be a result of them not being given an enforced time limit as the students were.

So, how can we go about answering the question? It takes some simple algebra. We can let g be the number of girls in the family and b be the number of boys.

Since Tegwen has the same number of sisters as brothers, we know g-1=b. We have to subtract 1 from g because Tegwen doesn’t count herself in her sisters, but she is included in the total number of girls.

We know that each of her brothers has 50 percent more sisters than brothers, so 3/2(b-1)=g.

We can put those two equations together to get b+1=3/2(b-1). By rearranging the equation, we can solve for b.

5=b

If we plug that back into our original formula, we can solve for g as well:

g=6

So, we know that the family has 5 boys and 6 girls, for a total of 11 children.

**Answer: 11**

Did you get it right? Try our other brain teasers.

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