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The sum of Joy's age and her brother's age is 24. Joy's brother's age is 3 years older than twice Joy's age. What is the difference between their ages?

Answer :

Let Joy be x years old

Joy's brother's age is 3 years older than twice joy's age.
Joy's Brother = 2x + 3

The sum of Joy's age and her brother's age is 24.
x + 2x + 3 = 24
3x + 3 = 24
3x = 24 - 3
3x = 21
x = 21 ÷ 3
x = 7

Joy:
x = 7

Brother:
2x + 3 = 2(7) + 3 = 17

Difference in their age = 17 - 7 = 10 years

They are 10 years apart.

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Rewritten by : Barada

Final answer:

Joy's age is found to be 7 years old, and her brother's age is determined to be 17 years old. The difference between their ages is therefore 10 years.

Explanation:

The question asks us to find the difference in age between Joy and her brother. Let's denote Joy's age as J. We know that Joy's brother is 3 years older than twice Joy's age, which we can write as 2J + 3. The equation representing their combined ages is J + (2J + 3) = 24.

To solve for Joy's age, we combine like terms and get 3J + 3 = 24. Subtracting 3 from both sides gives us 3J = 21, and dividing by 3 yields J = 7. Now that we know Joy's age, we can determine her brother's age: 2(7) + 3 = 17.

The difference between their ages is the brother's age minus Joy's age, which is 17 - 7 = 10 years.