P5 Math: Age Problem

Jane was thrice as old as Amy 4 years ago. 6 years later, the ratio of Jane's age to Amy's age will be 7:4. Find the ratio of Jane's age to Amy's age 2 years later.

Solution:

Two main things when we try solving age problem:

1. The age difference is fixed, always same.
2. The time reference is now.

Method 1: Using ratio

Four years ago
     Jane : Amy : Difference
=    3:1:2

(4+6) years = 10 years later, the ratio is
=   7:4:3

Difference is always same, so both ratios need to equalize using difference as the base.

3:1:2  --> 9u  : 3u : 6u 
7:4:3 --> 14u : 8u : 6u

14u - 9u = 5u --> 10 years (5u in 10 years), u = 2 years.

It means four years ago, Jane was 18 years old and Amy was 6 years old.
So two years later, Jane will be (18 + 4 + 2) = 26  years old and Amy (6+4+2) = 12 years old/

Ratio Jane : Amy = 24:12 = 2:1

Method 2: Using model

(1) Difference is always same --> d1 = d2 --> 2p = 3u, or p = 3/2u

(2) 3p + 10 = 7u

Now do substitution for p and solve the equation (2)

3p + 10 = 7u

--> 9/2u + 10 = 7u

--> 5/2u = 10

-->      u = 4

Six years later, Jane will be 7u = 28 years old and Amy will be 4u = 16 years old.

So in 2 years later Jane will be 28 - 4 = 24 years old, and Amy will be 16 - 4 = 12 years old.

Ratio Jane : Amy = 24:12 = 2:1