Problem Solving using Linear Systems

Question

Tom is twice as old as Jerry. In two years, Tom will be 4 times as Jerry was nine years ago. How old are they now?

Answer 1

Let T be Tom's age now.

And, J be Jerry's age now.

Today, Tom is twice as old as Jerry:

T = 2J

In two years from now, Tom will be 2 years older and he will also be 4 times the age that Jerry was 9 years ago:

T + 2 = 4 (J - 9)

We have a system of equations:

T = 2J

T + 2 = 4 (J - 9)

To solve the system of equation, we replace T in the second equation:

2J + 2 = 4 (J-9)

2J + 2 = 4J - 36

2J = 4J - 36 - 2

2J = 4J - 38

2J - 4J = -38

-2J = -38

J = -38 / -2

J = 19

And, we replace J in the first equation:

T = 2 (19)

T = 38

Now, Tom is 38 and Jerry is 19.

Answer 2

So first relationship, tom(T) is twice as old as Jerry(J)

Therefore T=2J

Next one, Tom will be 4 times order then jerry was 9 years ago in two years, therefore when jerry was 9 less years of age, Tom will be 4 times the 9 year less old Jerry. Two years in the future means both will be two years older, therefore since T and J are ages, we add two to both sides, which cancel out.

T+2=4*(J-9)+2

T=4(J-9)

replace T=2J in T=4*(J-9)

2J=4(J-9)

distribute the 4 to J and 9

this leads to

2J=4J-36

rearrange to J's are together and non variable numbers are together so

-4J on both sides, leads to

-2J=-36

therefore Jerry is 36/2( negatives cancel out) =>18

we know tom is 2x as old as Jerry so Tom will be 36 and Jerry is 18.