## Monday, May 30, 2011

### From an Indonesian Student

I am a Junior High School student in Jakarta. I am 12 years old now. I like solving maths word problems. I have a maths word problem that I cannot solve by myself.

In a housing estate there are 1000 couples.
2 / 3 of the husbands who are taller than their wives are also heavier.
3 / 4 of the husbands who are heavier than their wives are also taller.
If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller than their wives ?

I think the solution is 1000 - 120 = 880 husbands who are taller than their wives.
However, I am confused by the second and the third sentences in the word problem.

Made, 12-year old student in Indonesia

Yeap Ban Har writes: Let's start by assuming that a couple is made up of a husband and a wife. You may want to try to make a table (see photo - to be attached soon)

Also wife taller and heavier than husband means the same as husband shorter and lighter than wife.

Let's assume a husband is either heavier than or lighter than. It is possible that they have the same weight (mass) but let's not deal with that.

Can you continue?
(Note: Made has since replied that he was able to continue and solved the problem. See Comments for another suggested solution.)

Anyone would like to offer other solutions?

#### 1 comment:

1. Let X = the number of husbands who are taller than their wives (this is the number we are trying to find). Let Y = number of husbands who are heavier than their wives.

We know that 120 wives are taller AND heavier than their husbands. This means that 120 husbands are shorter AND lighter than their wives, and 880 husbands are EITHER taller OR heavier than their wives.

The problem as written supplies the following information:

(1) Husband taller (includes husbands who are taller AND heavier) = X

(2) Husband taller AND heavier = 2/3 X

(3) Husband heavier (includes husbands who are heavier AND taller) = Y

(4) Husband heavier AND taller = 3/4 Y

Note that statements (2) and (4) are identical. This means that 2/3X = 3/4 Y. Solving this equation for Y means that Y = 8X/9.

We know that (the number of husbands who are X) plus (the number of husbands who are Y) minus (the number who are both X AND Y) = 880 (from the second paragraph above). This means that:

X + Y – 2/3X = 880 (since the number who are X AND Y = 2/3 X = 3/4 Y)

Which can also be expressed as:

9X/9 + 8X/9 – 6X/9 = 880 (since Y = 8X/9 and 2/3X is the same as 6/9X)

Solving for X gives:

X = (9 * 880) divided by 11 = 720.

Thus the number of husbands who are taller then their wives is 720