The ratio of Maggie's age now to her brother Steven's age now is 2:3. In ten years, the ratio of their ages will be 4:5. How old in Maggie now? Do not label years old in your answer.

Maggie is currently 10 years old.

Explanation:

M = Maggie's age today

S = Steven's age today

The ratio of their current ages, specifically Maggie's age to Stevens age, is 2:3. So 2/3 = M/S

We can cross multiply to get 2S = 3M and divide both sides by 2 getting S = 3M/2 = 1.5M

So whatever Maggie's age is, we multiply by 1.5 to get Steven's age. This only applies to their current present day ages.

In 10 years, Maggie will be M+10 years old and Steven will be S+10 years old.

The ratio of their ages at this point in time is 4:5, so,

4/5 = (M+10)/(S+10)

4(S+10) = 5(M+10) cross multiply

4S+40 = 5M+50

4S-5M = 50-40

4S-5M = 10

4(1.5M) - 5M = 10 plug in S = 1.5M

6M - 5M = 10

M = 10

Maggie is currently 10 years old.

Extra info:

Use the value of M to find S.

S = 1.5*M

S = 1.5*10

S = 15

So Steven is currently 15 years old.

The ratio of Maggie's current age to Steven's current age is M/S = 10/15 = 2/3 which turns into 2:3

In 10 years, Maggie will be M+10 = 10+10 = 20 and Steven will be S+10 = 15+10 = 25

The ratio of their ages now is (M+10)/(S+10) = 20/25 = 4/5 leading to the ratio 4:5

This confirms our answers.

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