Two crews were assigned the job of setting a total of 960 conduit hangers. By the time the job was completed, one crew had set only 7/8 as many conduit hangers as the other crew. How many conduit hangers were set by the slower group?
Were did you get 15/8 from?
Let's assume the number of conduit hangers set by the slower group is x.
The faster group set 7/8 as many conduit hangers as the slower group. Therefore, the number of conduit hangers set by the faster group is (7/8)x.
The total number of conduit hangers set by both crews is 960.
So, we have the equation:
x + (7/8)x = 960
To solve the equation, let's first add the x terms:
(8/8)x + (7/8)x = 960
Now, we can combine the terms on the left side:
(15/8)x = 960
To isolate x, let's multiply both sides of the equation by the reciprocal of 15/8, which is 8/15:
(8/15)(15/8)x = (8/15)(960)
x = 512
Therefore, the slower group set 512 conduit hangers.
To find out how many conduit hangers were set by the slower group, we need to follow these steps:
Step 1: Determine the number of conduit hangers set by the faster group.
Let's assume the number of conduit hangers set by the faster group is x.
Step 2: Calculate the number of conduit hangers set by the slower group.
According to the problem, the slower group set only 7/8 as many as the faster group.
So, the number of conduit hangers set by the slower group would be (7/8) * x.
Step 3: Add the number of conduit hangers set by both groups.
Since the total number of conduit hangers set by both crews is 960, we can write an equation:
x + (7/8) * x = 960.
Step 4: Solve the equation for x.
Combining like terms, we get:
(15/8) * x = 960.
To isolate x, we can multiply both sides of the equation by (8/15):
x = 960 * (8/15).
Step 5: Calculate the value of x.
Performing the calculations, we find:
x = 512.
Step 6: Determine the number of conduit hangers set by the slower group.
To find the number of conduit hangers set by the slower group, substitute the value of x back into the equation:
(7/8) * x = (7/8) * 512.
Calculating this, we get:
(7/8) * 512 = 7 * 64 = 448.
Therefore, the slower group set a total of 448 conduit hangers.
so let the amounts be x and 7/8 x
x + 7/8 x = 960
15/8 x = 960
...