math
posted by crissy on .
Ben ran up threefourths of the steps three at a time, onesixth 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?

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.