Mrs. Smith is currently 27 years older than her daughter Kate. In 8 years Mrs. Smith will be twice as old as Kate. How old are Mrs. Smith and Kate and how old will they be in 8 years?
2 Answers
Kate is 19 years old and Mrs. Smith is 46 years old now.
Explanation:
Suppose the age of Kate at present =
Then age of Mrs. Smith now =
Now after 8 years the age of Mrs. Smith will be twice as that of Kate.
After 8 years, the age of Kate =
and, age of Mrs. Smith =
As Mrs. Smiths's age will be twice as that of Kate after 8 years so, twice the age Kate will make it equal to Mrs. Smiths's age at that time.
Writing that in equation form,
2(
or,
Bringing the x terms together and the number terms together
or,
Therefore, Mrs. Smiths's age now =
You can check your answer by adding 8 years to both ages and see that Mrs. Smith's age is twice that of Kate after 8 years.
See a solution process below"
Explanation:
First, let's call Mrs. Smith's age:
Now we know from above Mrs. Smith is 27 years older than Kate so we can write:
We also know in 8 years Mrs. Smith will be twice as old as Kate so we can write:
We can now substitute
We can now substitute
Mrs. Smith is 46 and Kate is 19
In 8 years Mrs Smith will be 54 and Kate will be 27
