Final answer:
David climbed a total of 261 stairs based on the given information.
Step-by-step explanation:
To solve this problem, we need to find the number of stairs David climbs based on the given information. We're told that David trips every two out of nine stairs. This means that for every 9 stairs, he trips on 2 of them. To find the fraction of stairs he trips on, we can simplify the ratio 2:9. We divide both the numerator and denominator by their greatest common factor, which is 1 in this case. So, the simplified ratio is 2:9.
Now, we know that for every 2 out of 9 stairs, David trips. And we know that he trips for the 58th time. So, we can set up a proportion to find the total number of stairs he climbs:
2 / 9 = 58 / x
Cross-multiplying, we get:
2x = 9 * 58
Simplifying, we have:
2x = 522
Dividing both sides by 2, we find:
x = 261
Therefore, David climbed a total of 261 stairs.