Question

Michelle is two years older than her sister Nicole. 10 years ago, Michelle was twice as old as her sister. How old is Michelle now? Use guess and check to solve this problem.

Answer 1

n+2=m m=12+2=14

Explanation:

M=N+2

M-10=(n-10)2

m-10=2n-20

m=2n-10

n+2=2n-10

n=2n-12

n-12=0

n=12

Answer 2

Michelle is 14 years old.

Explanation:

The only logical explanation for the two being two years apart in age and Michelle being twice as old ten years ago is if Michelle was 4 years old and Nicole was 2 years old ten years ago. To verify this, we can use a System of equations.

Let:
N = Nicole's Age

M = Michelle's Age

N + 2 = M

2n-10 = M

Since both equal Michelle's age, we can make a two step equation out of it.

N + 2 = 2n - 10

2 = N - 10

12 = N

We've found Nicole's age, allowing us to plug the answer back into the variable to get Michelle's.

N + 2 = M

12 + 2 = 14