Two crews were assigned the job of setting 900 fence posts. By the time the job was completed, one crew had set only 7/8 as many fence posts as the other crew. How many fence posts were set by the faster group?
If the faster group set x posts, then
x + 7/8 x = 900
Or, if the faster group set 8n posts, then the slower group set 7n posts.
8n + 7n = 900
Let's assume that the number of fence posts set by the faster crew is x.
According to the given information, the slower crew set 7/8 as many fence posts as the faster crew.
So, the number of fence posts set by the slower crew is (7/8)x.
The total number of fence posts set by both crews is 900.
Therefore, we can write the equation: x + (7/8)x = 900.
Combining the x and (7/8)x terms, we get (15/8)x = 900.
To solve for x, we can multiply both sides of the equation by 8/15:
(8/15)(15/8)x = (8/15)(900).
Simplifying, we find x = 480.
Therefore, the faster crew set 480 fence posts.
To find out how many fence posts were set by the faster group, we need to compare the number of posts set by both crews.
Let's assume the number of posts set by the faster crew is x.
According to the problem, the slower crew set 7/8 times x number of posts.
So, the number of posts set by the slower crew is (7/8) * x.
Now we have the total number of posts set by both crews. The problem states that a total of 900 posts were set.
Therefore, x + (7/8) * x = 900
To solve this equation, we can combine like terms:
(8/8) * x + (7/8) * x = 900
(15/8) * x = 900
To isolate x, we can multiply both sides of the equation by (8/15):
x = (900 * 8) / 15
x = 4800 / 15
x = 320
Therefore, the faster crew set 320 fence posts.