Brody is 3 years older than Janet. In 5 years the sum of their ages will be 65. How old is Brody now?

Answer 1

Let b be Brody's age and j be Janet's age.

b = j+3

b+5 + j+5 = 65

j+3 +5 + j+5 = 65

2j +13 = 65

2j = 52

j = 26

b = 26+3 = 29

Answer 2

Hi Kaylynn, based on the word problem, you can create two equations. First we will create variables, where B will represent Brady's age, and J will be Janet's age.

From the first sentence, we know Brody is 3 years older than Janet, so B = J + 3 (Equation 1).

From the second sentence, we know in 5 years the sum of their ages will be 65, so (B + 5) + (J + 5) = 65 (Equation 2).

Let's first simplify Equation 2 so all the non-variables are on the right side of the equation.

B + 5 + J + 5 = 65

Add the two 5s on the left.

B + J + 10 = 65

Subtract 10 from both sides.

B + J = 55 (New Equation 2)

Now we have a few options to solve, but I will use the Substitution method for this example. From Equation 1, we know B = J + 3, so we will plug in 'J + 3' into the New Equation 2 in place of 'B'. You will get:

(J + 3) + J = 55

Then let's drop the parentheses and add the J's to get,

2J + 3 = 55.

Subtract out 3 from both sides.

2J = 52.

Divide both side by 2.

J = 26.

Since the question asks for Brody's age, we can use equation 1 again knowing Janet is 26.

B = J + 3

Plug in 26 for J.

B = 26 + 3 = 29

Brody is currently 29.

You can confirm you have the correct answer by plugging both J = 26 and B = 29 into Equation 2, and you will see you get a true result.