To solve the problem of finding two consecutive even numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that their sum is 94 and [tex]\(b\)[/tex] is [tex]\(a + 2\)[/tex], follow these steps:
1. Understand the Problem:
- We are given that [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are two consecutive even numbers.
- We are given the relationship between [tex]\(a\)[/tex] and [tex]\(b\)[/tex]: [tex]\(b = a + 2\)[/tex].
- We are also given the equation: [tex]\(a + b = 94\)[/tex].
2. Set Up the Equations:
- From the relationship, [tex]\(b = a + 2\)[/tex].
- From the sum, [tex]\(a + b = 94\)[/tex].
3. Substitute [tex]\(b\)[/tex] in the Sum Equation:
- Substitute [tex]\(b = a + 2\)[/tex] into the sum equation [tex]\(a + b = 94\)[/tex]:
[tex]\[
a + (a + 2) = 94
\][/tex]
4. Simplify the Equation:
- Combine like terms:
[tex]\[
a + a + 2 = 94
\][/tex]
[tex]\[
2a + 2 = 94
\][/tex]
5. Solve for [tex]\(a\)[/tex]:
- Isolate [tex]\(a\)[/tex] by first subtracting 2 from both sides of the equation:
[tex]\[
2a + 2 - 2 = 94 - 2
\][/tex]
[tex]\[
2a = 92
\][/tex]
- Divide both sides by 2 to solve for [tex]\(a\)[/tex]:
[tex]\[
\frac{2a}{2} = \frac{92}{2}
\][/tex]
[tex]\[
a = 46
\][/tex]
6. Find [tex]\(b\)[/tex]:
- Use the relationship [tex]\(b = a + 2\)[/tex] to find [tex]\(b\)[/tex]:
[tex]\[
b = 46 + 2
\][/tex]
[tex]\[
b = 48
\][/tex]
Therefore, the two consecutive even numbers are [tex]\(a = 46\)[/tex] and [tex]\(b = 48\)[/tex].
