Answer:
Ruby worked 18 hours, Isaac worked 12, and Svetlana worked 72
Step-by-step explanation:
let:
- r : the amount of hours ruby worked
- i : the amount of hours isaac wcorked
- s : the amount of hours svetlana worked
given:
1) ruby worked 6 hours more than isaac
this translates to equation (1) r = i + 6
2) svetlana worked 4 times as many hours as ruby
this translates to equation (2) s = 4 * r
3) Together they worked 102 hours
this translates to r + i + s = 102 for equation (3)
Now, isolate i from (1) to get i = r - 6, and replace i in (3) using this:
r + (r - 6) + s = 102.
This equals -> 2r + s = 102 + 6 -> 2r + s = 108
replace s here with s from (2): 2r + (4*r) = 108
this equals 6*r = 108, from here, isolate r: r = 108/6 = 18
we know that i = r - 6. So i = 18 - 6 = 12
And s = 4*r = 4*18 = 72
verify that this works -> 72 + 18 + 12 = 102.
