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?
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.
To find out how many steps Ben ran up in total, we need to calculate the sum of the steps he ran up in each scenario.
First, let's calculate how many steps he ran up three at a time:
Ben ran up three-fourths of the steps three at a time. This means he ran up 3/4 * total steps three at a time.
To find out how many steps he ran up three at a time, we multiply 3/4 with the total number of steps.
Next, let's calculate how many steps he ran up two at a time:
Ben ran up one-sixth of the steps two at a time. So he ran up 1/6 * total steps two at a time.
We multiply 1/6 with the total number of steps to find out how many steps he ran up two at a time.
Finally, let's calculate how many steps he ran up one at a time:
He ran up the final 10 steps one at a time.
To find the total number of steps, we add up the number of steps in each scenario.
Let's assume the total number of steps is "x".
1. Steps ran up three at a time: 3/4 * x
2. Steps ran up two at a time: 1/6 * x
3. Steps ran up one at a time: 10
To find the total number of steps, we sum the three scenarios:
Total steps = (3/4 * x) + (1/6 * x) + 10
Now you can substitute the value of "x" (the total number of steps) into this equation and calculate the total steps Ben ran up.