Solve system, age problems?

Question

Tom is 4 times as old as Todd. In 6 years Tom's age will be 10 years more than 2 times as old as Todd. Please explain step by step? I have to explain it to someone else. Thank you.

Answer 1

i'll tell you how to set up the problem.

Lets call tom's age X, and Todd's age Y.

We are told that tom is 4 times as old as Todd, so
x=4y., for example if todd is 1 year old, tom is 4.
then we are told that in 6 years tom's age will be 10 years more than 2times as old as todd.

if x is tom's age, in six years he will 6+x,
and we are told that age will be 10 year more than 2 times todds age,

so x+6= 10+2y

so our two equations are x=4y and (x+6)=(10+2y)
The next step is to plug in 4y into x for the second equation and solve for y, then plug that number back ito x=4y to get x.


edit
After reading what someone else posted, I realized I made a mistake but in the spirit of honesty i wont change it just to get the points.

Answer 2

tom is 32 years old and todd is 8 years old

suppose that tom age is x and todd age is y

x=4y because tom is 4 times as old as todd
and
x+6=2(y+6)+10 because in 6 years tom's age will be 10 years more than 2 times as old as Todd

so we have 2 equation
x=4y
x+6=2(y+6)+10

by solving those 2 equations
4y+6=2y+12+10
2y=16
y=8
therefore x=4*8=32

Answer 3

Let
x = Tom's age now
y = Todd's age now

We have

x = 4y
x + 6 = 2(y + 6) + 10 = 2y + 12 + 10 = 2y + 22

Subtract the second equation from the first.

-6 = 2y - 22
16 = 2y
8 = y

x = 4y = 4*8 = 32

Tom is 32 and Todd is 8.