Mary is 15 years older than her niece Katie. In 10 years Mary is two times as old as Katie. How old are Mary and Katie now?
How do I solve this (equation + work)
Thank you!
Katie's age -- x
Mary's age -- x+15
10 years from now:
Katie : x+10
Mary : x+15 + 10 = x + 25
"Mary is two times as old as Katie" ---> 2x+25 = 2(x+10)
should be easy to solve
To solve this problem, let's assign variables to represent Mary's and Katie's ages.
Let's say Mary's current age is M, and Katie's current age is K.
We know that Mary is 15 years older than Katie, so we can write the equation: M = K + 15.
In 10 years, Mary will be M + 10 years old, and Katie will be K + 10 years old.
According to the problem, in 10 years, Mary will be two times as old as Katie. This can be expressed as the equation: M + 10 = 2(K + 10).
We now have a system of two equations:
M = K + 15
M + 10 = 2(K + 10)
We can solve this system of equations using the substitution method:
From the first equation, we can solve for M:
M = K + 15
Now substitute M = K + 15 into the second equation:
(K + 15) + 10 = 2(K + 10)
Simplify:
K + 25 = 2K + 20
Rearrange the equation to isolate K:
K - 2K = 20 - 25
-K = -5
K = 5
Now substitute the value of K back into the first equation to find M:
M = 5 + 15
M = 20
Therefore, Mary is currently 20 years old, and Katie is currently 5 years old.