To solve the problem of finding Jeremy and Ervin's current ages, we can follow these steps:
### Understanding the Problem
1. Set Variables:
- Let [tex]\( E \)[/tex] represent Ervin's current age.
- Since Jeremy is 3 years older than Ervin, Jeremy's current age will be [tex]\( E + 3 \)[/tex].
2. Future Ages:
- In seven years, Ervin's age will be [tex]\( E + 7 \)[/tex].
- In seven years, Jeremy's age will be [tex]\( (E + 3) + 7 = E + 10 \)[/tex].
3. Sum of Future Ages:
- The sum of their ages in seven years is given to be 39.
- Form an equation based on this information: [tex]\( (E + 7) + (E + 10) = 39 \)[/tex].
### Solve the Equation
4. Simplify the Equation:
- Combine like terms: [tex]\( E + 7 + E + 10 = 39 \)[/tex]
- This simplifies to: [tex]\( 2E + 17 = 39 \)[/tex]
5. Isolate the Variable [tex]\( E \)[/tex]:
- Subtract 17 from both sides of the equation: [tex]\( 2E = 39 - 17 \)[/tex]
- Simplifying gives: [tex]\( 2E = 22 \)[/tex]
6. Solve for [tex]\( E \)[/tex]:
- Divide both sides by 2: [tex]\( E = \frac{22}{2} \)[/tex]
- This simplifies to: [tex]\( E = 11 \)[/tex]
### Determine Their Present Ages
7. Find Jeremy's Age:
- Substitute the value of [tex]\( E \)[/tex] back to find Jeremy's age: Jeremy's age = [tex]\( E + 3 = 11 + 3 \)[/tex]
### Final Answer
- Ervin's current age is [tex]\( 11 \)[/tex] years old.
- Jeremy's current age is [tex]\( 14 \)[/tex] years old.
