Math Problem x6

Question

The sum of the ages of Wyatt and Natalie is 52 years. 8 years ago, Wyatt's age was 2 times Natalie's age. How old is Wyatt now?

Answer 1

Hello, Bon,

We can make two equations from the two comparisons of ages. Let the ages for Wyatt and Natalie be W and N.

We know that W+N=52.

Eight years ago their ages would be

W-8, and N-8. At that time we are told that:

(W-8)/(N-8)=2 Wyatt's age was twice that of Natalie 8 years ago.

We can rearrange this last equation and solve for W, which is 2N-8,

Substitute that into the first equation: 2N-8+N=52

Solve for N (= 20). Now find W: W= (52-20) = 32

Natalie is 20 and Wyatt is 32.

Bob

Answer 2

W+N = 52

W-8 = 2(N-8) = 2N-16

W = 2N -16+8 = 2N -8

W = 2N -8

W = -N+52 subtract to get

0 = 3N-60

N = 60/3 = 20 years old for Natalie

W = 52-20 = 32 years old for Wyatt

8 years ago they were 12 and 24, 24 was twice 12

Answer 3

Let W be Wyatts Age

Let N be Natalies Age

The sum of Wyatt and Natalies Age equals 52 today : W+N=52 (EQN 1)

8 years ago, both will be 8 years younger, thus we will subtract 16 (2 times 8) years from the sum...

W+N= 52-16= 36 (EQN 2) (Sum of Wyatt and Natalies Ages 8 years Ago equals 36)

W=2N (EQN 3) (8 Years ago, Wyatt's ages equaled two times Natalies Age)

We can use EQN 2 to solve for W in terms of N 8 years Ago

W=36-N

We can then plug this into EQN 3 to solve for Natalies age 8 years ago

36-N=2N

36=3N

N=12 8 Years Ago

Now that we know Natalie was 12, 8 years ago, we can plug this into EQN 3 to find Wyatts age 8 years ago

W=2*12= 24 (8 Years Ago)

Now add 8 years to both ages to find out their age today

N=20 Today

W= 32 Today

To check our answer, we plug the ages today into EQN 1

Check: 20+32=52

Wyatts age today is 32 years