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
MJ
Dec 19, 2017

Kate is 19 years old and Mrs. Smith is 46 years old now.

Explanation:

Suppose the age of Kate at present = x
Then age of Mrs. Smith now = x+27

Now after 8 years the age of Mrs. Smith will be twice as that of Kate.

After 8 years, the age of Kate = x+8
and, age of Mrs. Smith = x+27+8
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(x+8) = x+27+8
or, 2x + 16 = x + 35

Bringing the x terms together and the number terms together

2x-x = 35-16
or, x = 19
Therefore, Mrs. Smiths's age now = x+27 = 19+27 = 46 years

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.

smendyka
Dec 19, 2017

See a solution process below"

Explanation:

First, let's call Mrs. Smith's age: s and we can call Kate's age: k

Now we know from above Mrs. Smith is 27 years older than Kate so we can write:

s = k + 27

We also know in 8 years Mrs. Smith will be twice as old as Kate so we can write:

s + 8 = 2(k + 8)

We can now substitute (k + 27) from the first equation for s in the second equation and solve for k:

s + 8 = 2(k + 8) becomes:

(k + 27) + 8 = 2(k + 8)

k + 27 + 8 = (2 xx k) + (2 xx 8)

k + 35 = 2k + 16

-color(red)(k) + k + 35 - color(blue)(16) = -color(red)(k) + 2k + 16 - color(blue)(16)

0 + 19 = -color(red)(1k) + 2k + 0

19 = (-color(red)(1) + 2)k

19 = 1k

19 = k

k = 19

We can now substitute 19 for k in the first equation and calculate s:

s = k + 27 becomes:

s = 19 + 27

s = 46

Mrs. Smith is 46 and Kate is 19

In 8 years Mrs Smith will be 54 and Kate will be 27

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