Name ______Date ______

Multi-Step Equations

  1. The perimeter of a triangle is 51cm.The lengths of its sides are consecutive odd integers. Find the lengths of all three sides.
Let x = first integer, x + 2 = 2nd and x + 4 = the 3rd.
x + x+2 + x + 4 = 51
15,17,19 ANSWER
  1. Consecutive integers that follow each other in order. You want to find three consecutive integers whose sum is 84.
Answer: 27,28,29
  1. A gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited use and $6 per day for equipment rental. Write and solve an equation to find how many times you must use the gym to justify becoming a member.
16x + 8x = 450 + 6x
When x = 25, they are equal. You would have to go 26 times to Justify being a member.
  1. Cover Design: You want the cover of a sports magazine to show two photos across its width. The cover is 6 ½ inches wide, and the left and right margins are each ¾ inch. The space between the photos is ½ inch. How wide should you make the photos?
  • Draw a diagram of the cover.
  • Write an equation to model the problem. Use your diagram to help.
  • Solve the equation and answer the question.
DRAW A PICTURE
6.50 = .5 + .75 + .75 + 2x
solve for x to get 2.25 each picture.
  1. Language classes: At Franklin High School, 45 students are taking French. This number has been increasing at a rate of 3 students per year. The number of students taking Spanish is 108 and has been decreasing at a rate of 4 students per year. At these rates, when will the number of students taking French equal the umber taking Spanish?
  • Write and solve an equation to answer the question.
  • Check your answer with a table
45 + 3x = 108 – 4x
x = 9 years.
  1. Two friends are 60 miles apart. They decide to ride their bicycles to meet each other. Sally starts from the college and heads east, riding at a rate of 21 miles per hour. At the same time, Teresa starts from the river and heads west, riding at a rate of 15 miles per hour.
  • Draw a diagram showing the college and the river 60 miles apart and the two friends riding toward each other.
  • How far does each cyclist ride in t hours.
  • When the two cyclists meet, what must be true about the distances they have ridden? Write and solve an equation to find when they meet.
21t + 15t =60
t = 1.67 hours.( or 1 hour and 40 minutes).
The two distances must add to 60. If you plug in 1 2/3 for t, you will see that this is true.