One month, ruby worked 6 more hours than isaac, and Svetlana worked 4 times as many hours as ruby. together they worked 126 hours / whats the number of hours each person worked

Let's begin by assigning letters to represent our unknowns:

R (hours Ruby worked)

I (hours Isaac worked)

S (hours Svetlana worked)

Now let's see if we can express all three unknowns in terms of one unknown, according to the facts given in the problem:

R = I + 6 (Ruby worked 6 more hours than Isaac)

S = 4R (Svetlana worked 4 times more hours than Ruby)

We can see that we can express the hours Isaac worked in terms of Ruby:

R = I + 6, therefore, I = R - 6

Now we have all three unknowns expressed in terms of one unknown (R). Now we can write an equation to express the given sum of their worked hours (126) in terms of our expressions for one unknown (R):

R + (R - 6) + 4R = 126

Now let's solve our equation for the value of R and then use our expressions for R to calculate the values for I and S:

R + R - 6 + 4R = 126

6R - 6 = 126

6R = 126 + 6

6R = 132

R = 132/6

R = 22 (hours Ruby worked)

I = R - 6

I = 22 - 6

I = 16 (hours Isaac worked)

S = 4R

S = 4 (22)

S = 88 (hours Svetlana worked)

Finally, let's check our three answers to see if their sum is 126 (the given total of hours worked):

22 + 16 + 88 = 38 + 88 = 126

We see that they do, so we are confident that our answers are correct.

The trick to solving this problem was realizing that we could express three unknowns in terms of one unknown to give us a solvable equation.