Question

Mary is currently 19 years older than her cousin Courtney. In 5 years she will be 2 times as old as Courtney. Let c be Courtney’s age and solve for both of their ages.

Answer 1

Courtney's age is 14 years and Mary's age is 33 years.

Explanation:

Since Mary is currently 19 years older than Courtney, we can express Mary's age as c + 19.

In 5 years, Mary will be 2 times as old as Courtney, which means that she will be 2 * c years old.

Since Mary will be 2 * c years old in 5 years, we can express this as (c + 19) + 5 = 2 * c.

Solving this equation for c, we get:

c + 19 + 5 = 2 * c

c = 14

Substituting this value of c back into the equation c + 19 = Mary's age, we get:

14 + 19 = Mary's age

Mary's age = 33

Therefore, Courtney's age is 14 years and Mary's age is 33 years.

Answer 2

Explanation:

To solve this problem, we can set up a system of two equations to represent the information given in the problem.

Let c be Courtney's age.

The first equation is:

c + 19 = x

This equation represents the fact that Mary is currently 19 years older than Courtney.

The second equation is:

c + 5 = 2 * (c + 5)

This equation represents the fact that in 5 years, Mary will be twice as old as Courtney.

We can solve for both of their ages by solving this system of equations.

First, let's solve the second equation for c:

c + 5 = 2 * (c + 5)

c + 5 = 2c + 10

-c = 5

c = -5

This solution is not valid, because Courtney's age cannot be negative.

Therefore, the only solution to this system of equations is:

c = 0

x = 19

This means that Courtney is currently 0 years old, and Mary is currently 19 years old.