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The sum of Joy's age and her brother's age is 24. Her brother's age is 3 years older than twice Joy's age.

What is the difference, in years, between Joy's age and her brother's age?

A. 4

B. 6

C. 10

Answer :

To solve the problem, we need to find the difference in years between Joy's age and her brother's age. Let's break it down step-by-step:

1. Define Variables:
- Let Joy's age be [tex]\( j \)[/tex].
- Let her brother's age be [tex]\( b \)[/tex].

2. Set Up Equations:
- We know from the problem that the sum of their ages is 24:
[tex]\[
j + b = 24
\][/tex]

- We also know that her brother's age is 3 years older than twice Joy's age:
[tex]\[
b = 2j + 3
\][/tex]

3. Substitute and Solve:
- Substitute [tex]\( b = 2j + 3 \)[/tex] into the first equation:
[tex]\[
j + (2j + 3) = 24
\][/tex]
- Simplify this equation:
[tex]\[
3j + 3 = 24
\][/tex]

4. Solve for Joy's Age:
- Subtract 3 from both sides:
[tex]\[
3j = 21
\][/tex]
- Divide by 3:
[tex]\[
j = 7
\][/tex]

5. Find Her Brother's Age:
- Use the equation [tex]\( b = 2j + 3 \)[/tex]:
[tex]\[
b = 2(7) + 3 = 14 + 3 = 17
\][/tex]

6. Calculate the Difference in Ages:
- The difference between her brother's age and Joy's age is:
[tex]\[
b - j = 17 - 7 = 10
\][/tex]

Therefore, the difference in years between Joy's age and her brother's age is 10 years.

The correct answer is C 10.

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