Question

Emily is 6 years older than Daniel. One-fifth of Emily’s age a year ago added to three-fourths of Daniel’s age is equal to Daniel’s age. How old is Emily? Show your work.

a) Emily is 24 years old.
b) Emily is 30 years old.
c) Emily is 36 years old.
d) Emily is 18 years old.

Answer 1

To find Emily's age, we need to set up and solve an equation using the given information.

Step-by-step explanation:

Let's represent Daniel's age as x. According to the problem, Emily is 6 years older than Daniel, so we can say that Emily's age is x + 6.

A year ago, Daniel's age would have been x - 1 and Emily's age would have been (x + 6) - 1.

The problem states that one-fifth of Emily’s age a year ago added to three-fourths of Daniel’s age is equal to Daniel’s age. So we can write the equation:

(1/5)((x + 6) - 1) + (3/4)(x - 1) = x

Simplifying and solving this equation will give us the value of x, which represents Daniel's age. Once we know Daniel's age, we can find Emily's age by adding 6 to it.

After solving the equation, we find that x = 18, which means Daniel is 18 years old. Therefore, Emily is 18 + 6 = 24 years old. So the correct answer is option a) Emily is 24 years old.