Answer:
44 hours
Step-by-step explanation:
1. Identify
Unknown:
- The number of hours Jessica works in a week.
- The total number of hours Jessica and Mary work in a week.
Known:
- Mary works 26 hours in a week.
- Jessica works eight less hours per week than Mary.
2. Strategize
- Let x be the number of hours Mary works in a week.
- If Jessica works eight less hours per week than Mary then:
⇒ Hours Jess works = x - 8
- Let y be the total number of hours the two work in a week.
3. Set Up
Total hours = Hours Mary works + Hours Jessica works
⇒ y = x + x - 8
⇒ y = 2x - 8
4. Solve
Mary works 26 hours in a week ⇒ x = 26.
Substitute x = 26 into the equation and solve for y:
⇒ y =2x - 8
⇒ y =2(26) - 8
⇒ y =52 - 8
⇒ y = 44
5. Check
Verify by substituting the solution y = 44 into the original equation:
⇒ 44 = 2x - 8
⇒ 44 + 8 = 2x - 8 + 8
⇒ 52 = 2x
⇒ 52 ÷ 2 = 2x ÷ 2
⇒ 26 = x
⇒ x = 26
As x = 26 and Mary works 26 hours per week, the solution y = 44 is verified.
6. Present
If Mary works 26 hours a week, and Jessica works eight less hours per week than Mary, the total hours the two work in a week is 44 hours.
