# math

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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

(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.

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