Question

Today, Meg’s age is 3/4 of Tracy’s age. In 5 years, Meg’s age will be 4/5 of Tracy’s age. How old is Tracy today?

Answer 1

Tracy is 20

Explanation:

Meg is now 3/4 of Tracy's age. In 5 years, she will be 4/5 of Tracy's age. You want to know Tracy's age.

Setup

Let m and t represent Meg's and Tracy's ages, respectively.

m/t = 3/4

(m+5)/(t+5) = 4/5

Solution

Using the first equation, we can write the expression for m:

m = 3/4t

Substituting that into the second equation gives ...

(3/4t +5)/(t +5) = 4/5

15t +100 = 16t +80 . . . . . . . multiply both sides by 20(t+5)

20 = t . . . . . . . . . . . . subtract 80+15t

Tracy is 20 years old today.

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Additional comment

We notice that the fraction 4/5 has numerator and denominator values that are each 1 greater than those in the fraction 3/4. This tells us that adding 5 years is the same as adding 1 ratio unit to each of the ages. Tracy's age is represented by 4 ratio units in the ratio 3/4, so her age now is 4·5 years = 20 years. We find this thinking a lot simpler than writing and solving equations.

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Answer 2

Answer: 20 years old

Explanation:

To solve this problem, we can use algebraic equations. Let's use 'T' to represent Tracy's age.

Meg's current age is 3/4 of Tracy's age, so Meg's age can be represented as (3/4)T.

In 5 years, Tracy's age can be represented as T + 5, and Meg's age can be represented as (3/4)T + 5.

Meg's age in 5 years will be 4/5 of Tracy's age, so we can write the equation as (3/4)T + 5 = (4/5)(T + 5).

Now, simplify the equation to solve for T.

(3/4)T + 5 = (4/5)(T + 5)

(3/4)T + 5 = (4/5)T + 4

1 = (1/20)T

T = 20