Question

One month, Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hours. Find the number of hours each person worked.

Answer 1

Answer/Step-by-step explanation:

Let x hours be the number of hours Issac worked

    x+6 hours be the number of hours Ruby worked

   4(x+6) hours be the number of hours Svetlana worked.

x + x + 6 + 4(x+6) = 126

x + x + 6 + 4x +24 = 126

                  6x +30 = 126

                         6x = 96

                           x = 16

Therefore, Issac worked 16 hours.

                 Ruby worked 16+6 = 22 hours

                 Svetlana worked 22 × 4 = 88 hours.

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Answer 2

Answer: Ruby: 22 hours, Isaac: 16 hours & Svetlana: 88 hours.

Step-by-step explanation:

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)