Age problem having a difficult time understanding equations

Question

Juwan is 3 years older than Erica. In 5 years the sum of their ages will be 53. How old is Juwan now?

Answer 1

Age problem having a difficult time understanding equations

Juwan is 3 years older than Erica. In 5 years the sum of their ages will be 53. How old is Juwan now?

Hello Brianna,

This equation says Juwan is Ericas age plus 3 more years.

J = E + 3

This equation we are adding more 5 years to both Juwan and Ericas age, and setting the sum of their ages equal to 53.

J + 5 + E + 5 = 53

Now, we substitute for J into the second equation, with E + 3 from the first equation.

E + 3 + 5 + E + 5 = 53

Solve for E

E + 3 + 5 + E + 5 = 53

2E + 13 = 53

2E = 40

E = 20

Since Erica is 20 years old, substitute her age into E from the first equation.

J = 20 + 3

J = 23

Juwan is 23 years old.

Answer 2

Juwan Age: x and Erica Age: y

Juwan is 3 years older than Erica: x = y + 3

In 5 years, Juwan age: x + 5 and Erica age: y + 5

In 5 years, Juwan age + Erica age = 53 ==> (x + 5) + (y + 5) = 53 ==> x + y = 53 - 10 ==> x + y = 43

x + y = 43 ==> (y + 3) + y = 43 ==> 2y = 43 - 3 ==> 2y = 40 ==> y = 20 (Erica Age)

x = y + 3 ==> x = 20 + 3 ==> x = 23 (Juwan Age)

Check: In 5 years, Juwan age + Erica age = 53

Juwan age + Erica age = 53 ==> (x + 5) + (y + 5) = 53 ==> (23 + 5) + (20 + 5) = 53 ==> 28 + 25 = 53 ==> 53 = 53