Volunteer Service Hours

(1) 16

Explanation

Analyze

• Students must complete 135 hours of volunteer Service (Given)
• Students work -30hour shifts (Given)
• A student has already completed 87 hours of Service (Given)
• How many more 3-hour shifts must she work? (Find)

Form

Let x = the number of shifts needed to complete the service requirement.  Since each shift is 3 hours long, multiplying 3 by the number of shifts will give the number of additional hours the students needs to volunteer.

(The number of hours she has already completed) plus 3 times (the number of shifts yet to be completed) is (the number of hours required)

87 + 3 · x = 135

Solve

• We need to isolate x on the left side
  • 87 + 3x = 135
• To isolate the variable term 3x, subtract 87 from both sides to undo the addition of 87
  • 87 + 3x - 87 = 135 - 87
• Do the subtraction
  • 3x = 48
• To isolate x, divide both sides by 3 to undo the multiplication by 3
  • \(\frac{3x}{3} = \frac{48}{3}\)
• Do the division
  • x = 16

State

The student needs to complete 16 more 3-hour shifts of volunteer service

Check

The student has already completed 87 hours.  if she works 16 more shifts, each 3 hours long, she will have 16 · 3 = 48 more hours.  Adding the two sets of hours, we get:

87 + 48 = 135 (which is the total number of hours needed)

The result, 16, checks