Question

7-49. for each problem, write one or two equations to represent the situation, define variable(s) and clearly answer the question.
the lees have three children. the oldest is twice as old as the youngest. the middle child is five years older than the youngest. if the sum of the ages is 57, how old is each child?

Explanation:

Step1: Define variables

Let $x$ = age of youngest child.
Then age of oldest = $2x$, age of middle = $x+5$.

Step2: Set up sum equation

Sum of ages equals 57:
$$x + (x+5) + 2x = 57$$

Step3: Simplify and solve for $x$

Combine like terms:
$$4x + 5 = 57$$
Subtract 5 from both sides:
$$4x = 52$$
Divide by 4:
$$x = \frac{52}{4} = 13$$

Step4: Calculate other ages

Oldest child: $2x = 2\times13 = 26$
Middle child: $x+5 = 13+5 = 18$

Answer:

Youngest child: 13 years old, Middle child: 18 years old, Oldest child: 26 years old