math

posted by .

Ben ran up three-fourths of the steps three at a time, one-sixth of the steps two at a time, and the final 10 steps one at a time. How many steps did Ben run up in all?

  • math -

    Let's write an equation to model this situation.

    Let s be the number of total steps.

    (3/4)s + (1/6)s + 10 = s
    Collect the s's on one side.

    10 = s - (3/4)s - (1/6)s
    Find a common denominator, 12 in this case.

    10 = (12/12)s - (9/12)s - (2/12)s
    Simplify.

    10 = s/12
    Multiply both sides by 12.

    120 = s

    Now let's check our answer.
    (3/4)s = (3/4)(120) = 90
    Is it divisible by 3? Yes, 90/3 = 30.

    (1/6)s = (1/6)(120) = 20
    Is it divisible by 2? Yes, 20/2 = 10.

    The answer is 120 steps.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 8th grade

    Laura is training her pet white rabbit, Sugar, to climb up a flight of 25 steps. Sugar can hop up one or two steps at a time. She never hops back down, only up. How many different ways can Sugar hop up the flight of steps?
  2. math

    Consider the following students method of solving the proportion 8/5 = 20/x and determine whether the methods were correct: Richie: First I divided 20 by 8 and got 2 1/2. Then I multiplied 2 1/2 by 5 and got 12 1/2 for my answer. Martha: …
  3. Math

    Alice, Beth, and Charlene start climbing a staircase, each with her left foot on step 1 and then her right foot on the next consecutive step. Alice climbs one step at a time, Beth two steps at a time, and Charlene three steps at a …
  4. math

    You have 2 floors, and there are 14 steps inbetween the two floors. you have a cat that can get to the top by either taking one step at a time or two steps. ( at one time going up the cat can take both one or two steps). How many possible …
  5. math

    Annie likes to walk 2 steps, jump 2 steps and then skip 2 steps. If she does this pattern over and over again for a total of 52 steps, how many jumping steps will she make?
  6. Quantum Physics

    Suppose we ran m steps of Grover's algorithm on some function f (which has one marked element y) and the resulting superposition was exactly |y⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial …
  7. physics

    Suppose we ran m steps of Grover's algorithm on some function f (which has one marked element y) and the resulting superposition was exactly |y⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial …
  8. Algebra

    Yazmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of …
  9. Math

    azmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of 60 …
  10. math

    mama rabbit hops 6 steps at a time, while baby rabbit hops 3 steps at a time. which steps will they hop together if they are 20 steps?

More Similar Questions