Simple fractions question

Mary and Henry shared a collection of stamps. Mary had 7/10 of the total number of stamps. If Mary gave 38 stamps to Henry, she will have thrice the number of stamps Henry have. How many stamps did Mary have?

By the way, we cannot use algebra to solve this question.

This is the entire question, because this is a primary school(5th Grade) question in Singapore, we can't use algebra to solve since they haven't learnt it.

• Then what can you use? – Gerry Myerson May 7 '13 at 13:04
• Algebra makes thing a lot simpler... – A. Chu May 7 '13 at 13:07
• As soon as you write $7/10$, you are using some algebra. – Julien May 7 '13 at 13:07

Note that to have three times as many stamps as Henry, Mary needs to end up with three quarters of the stamps, and Henry with one quarter. She starts off with 7/10 and gives some away, so she can't get three quarters.

If the stamps were given by Henry to Mary, she'd need her share of the total number of stamps to increase by 5%, or equivalently 1/20 of the total. So the total number of stamps is $38 \times 20$.

This avoids using symbolic algebra, but of course it is hidden just below the surface.

So if Mary there were a total of $s$ stamps, then Mary had $s\cdot 7/10$ - so how much did Henry have?

Now if they exchange, Mary will have $s\cdot 7/10 - 38$, how much will Henry have, and could you write down a relationship between how much each one has?

If you do everything right, you get a linear equation in one variable.

• That is the entire question, because this is a primary school(5th Grade) question in Singapore, we can't use algebra to solve since they haven't learnt it. – user2008436 May 7 '13 at 13:13
• @user2008436 I see, but a bit weird. My daughter learned solving 1st degree equations in 3rd grade (in the Russian math program), and I've heard the Singapore one is more advanced. Interesting. – gt6989b May 7 '13 at 13:15