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Jacob is 5 years older than Brenda was last year. In twenty four years, Brenda will be twice as old as Jacob is now. What is the sum of their ages? 1) Identify and label the unknown(s). 2) Write the equation. 3) Find the age(s). 4) Answer the question.

Respuesta :

stevenslusser

Answer:

Jacob = 20

Brenda = 16

Step-by-step explanation:

B = Brenda's age

J = Jacob's age

We know the following:

J = (B – 1) + 5

B + 24 = 2J

Solving the second equation for B:

B + 24 = 2J

B = 2J – 24

Substituting the result for B in the first equation:

J = (B – 1) + 5

J = [(2J – 24) – 1] + 5

Solving for J:

J = 2J – 24 – 1 + 5

J = 2J – 20

–J = –20

J = 20

Therefore, Jacob is 20 years old.

To find Brenda's age, we substitute 20 for J in the following:

B + 24 = 2J

B + 24 = 2(20)

B + 24 = 40

B = 16

Therefore, Brenda is 16 years old.

To verify:

We know Jacob is 5 years older than Brenda was last year. Brenda was 15 years old last year, and Jacob is 20 years old now. That's correct.

We also know, in 24 years, Brenda will be twice as old as Jacob is now. In 24 years, Brenda will be 40 years old. Twice Jacob's age now is 40 years old. That's also correct.

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