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QUESTION IMAGE

translate each statement into an equation. type the equations in use th…

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