Question

q20. four years ago tim was 4 times older than his brother matthew. in six years' time tim will only be double his brother's age. calculate how old the two brothers currently are.

Answer 1

By setting up a system of equations using the given information, we find that Tim is currently 24 years old and Matthew is 9 years old.

Step-by-step explanation:

To solve the problem of determining the current ages of Tim and Matthew, we set up a system of equations based on the information provided:

• Four years ago, Tim was 4 times older than Matthew.
• In six years, Tim will be twice as old as Matthew.

Let T represent Tim's current age and M represent Matthew's current age.

Based on the information:

1. T - 4 = 4(M - 4)
2. T + 6 = 2(M + 6)

Solving the first equation for T gives us:

T = 4M - 16 + 4

T = 4M - 12

Substitute T in the second equation:

(4M - 12) + 6 = 2M + 12

4M - 6 = 2M + 12

4M - 2M = 12 + 6

2M = 18

M = 9

Now we can find T:

T = 4(9) - 12

T = 36 - 12

T = 24

Thus, Tim is currently 24 years old and Matthew is 9.