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Math Warm-Up Exercises: Ratios, Percentages, and Interest Problems

A series of math problems involving ratios, percentages, and simple interest calculations. Topics include similar triangles, flagpole shadows, and solving for unknown variables in equations. Examples provided for practice and homework assignments.

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Math Warm-Up Exercises: Ratios, Percentages, and Interest Problems

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  1. Warm Ups • A student has completed 12 out of 34 homework assignments. At this rate, how many assignments would the student complete out of 85 assignments. • To make a model of the Victoria River, Zoe used 2.5 inches of clay for every 7 miles of the actual river’s length. Her model river was 50 inches long. How long is the Victoria River? Answers: • 30 • 140

  2. 4 - 4 PercentsDay 2 Objective: To solve ratio word problems and problems simple interest. Standard 5.0

  3. Similar Triangles (worksheet) 1. A vertical flagpole casts a shadow 12 ft long at the same time that a nearby vertical post 5 ft high casts a shadow 3 ft long. Find the height of the flagpole.

  4. Similar Triangles (worksheet) 2. A vertical rod 8 ft high casts a shadow 6 ft long. At the same time, a nearby tree casts a shadow 15 feet long. Find the height of the tree.

  5. Try #3 with partnerTry #4 on your own 3. 4. Finish this worksheet for homework!!

  6. Interest Think about these questions.. What is it? Where/When is it earned? Why? Now discuss your answers with a partner.

  7. I = prt I = Interest earned ($) p = principle (amount put in) ($) r = interest rate (as a decimal) (%) t = time (in years) (yrs)

  8. Example 1 Find p if I = $45, r = 6%, and t = ½ year 45 = p(0.06)(.5) 45 = .03p p = $1500

  9. TOO • Find p if I = $196, r = 10%, t = 7 years. • Find r if I = $120, p = $600, t = 5 years. Answers: • p = $280 • r = 4%

  10. Example 2 Find I if p = $1500, r = 7%, and t = 18 months *change months to years (÷ 12) I = 1500(.07)(18/12) I = 105(1.5) I = $157.50

  11. TOO • Find I if p = $500, r = 5%, t = 6 months. • Find t if I = $200, p = $1500, r = 1%. Answers: • I = $12.50 • t = 13.3 years = 13 years 4 months

  12. Homework Similar Triangles worksheet Pg. 219 # 40-45 all

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