Let's solve this step-by-step. We are given that Helly is 3 years older than Michele. Four years ago, the sum of their ages was 67. We need to determine their current ages.
### Step 1: Define Variables
Let's denote Michele's current age by [tex]\( x \)[/tex].
### Step 2: Express Helly's Age
Since Helly is 3 years older than Michele, Helly's current age will be [tex]\( x + 3 \)[/tex].
### Step 3: Ages Four Years Ago
Four years ago:
- Michele's age was [tex]\( x - 4 \)[/tex].
- Helly's age was [tex]\( (x + 3) - 4 = x - 1 \)[/tex].
### Step 4: Set Up the Equation
We know that the sum of their ages four years ago was 67. So, we can write the equation:
[tex]\[ (x - 4) + (x - 1) = 67 \][/tex]
### Step 5: Simplify the Equation
Combine like terms:
[tex]\[ x - 4 + x - 1 = 67 \][/tex]
[tex]\[ 2x - 5 = 67 \][/tex]
### Step 6: Solve for [tex]\( x \)[/tex]
Add 5 to both sides:
[tex]\[ 2x - 5 + 5 = 67 + 5 \][/tex]
[tex]\[ 2x = 72 \][/tex]
Divide by 2:
[tex]\[ x = 36 \][/tex]
### Step 7: Determine Their Current Ages
Since [tex]\( x = 36 \)[/tex]:
- Michele's current age is [tex]\( x = 36 \)[/tex].
- Helly's current age is [tex]\( x + 3 = 36 + 3 = 39 \)[/tex].
### Conclusion
Michele is currently 36 years old, whereas Helly is currently 39 years old.
