Question

translate each statement into an equation. type the equations in
use the 1st letter of each name as the variables.
then solve the system.
fred is 4 years older than wilma.

the sum of their ages is 28.

how old are they?
fred = years old
wilma = years old
question help: video

Explanation:

Step1: Define Variables

Let \( F \) be Fred's age and \( W \) be Wilma's age.

Step2: Translate First Statement

Fred is 4 years older than Wilma, so \( F = W + 4 \).

Step3: Translate Second Statement

The sum of their ages is 28, so \( F + W = 28 \).

Step4: Substitute \( F \) in Second Equation

Substitute \( F = W + 4 \) into \( F + W = 28 \):
\( (W + 4) + W = 28 \)
Simplify: \( 2W + 4 = 28 \).

Step5: Solve for \( W \)

Subtract 4 from both sides: \( 2W = 24 \)
Divide by 2: \( W = 12 \).

Step6: Solve for \( F \)

Substitute \( W = 12 \) into \( F = W + 4 \):
\( F = 12 + 4 = 16 \).

Answer:

First equation: \( F = W + 4 \)
Second equation: \( F + W = 28 \)
Fred = 16 years old
Wilma = 12 years old