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# Rate problem

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One month, Ruby worked 8 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked $$96$$ hours. Find the number of hours each person worked.

Apr 13, 2022

#1
+2541
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Write as a system of 3 equations:

$$r = 8+i$$                       (1)

$$s = 4r$$                            (2)

$$i+r+s=96$$              (3)

Rearrange (1) so $$i$$ is the independent variable: $$i = r - 8$$

Now, substitute i and s in terms of r: $$r + 4r + r-8 =96$$

Simplify: $$6r - 8 = 96$$

Add 8 to both sides: $$6r = 104$$

Divide by 6: $$r = 17 {1 \over 3}$$

Now substitute $$r$$ into (1) and solve for $$i$$$$17 {1 \over3} = 8 + i$$

Subtract 8 from both sides: $$i = 9 {1 \over3}$$

Now substitute $$r$$ into (2) and solve for $$s$$$$4 \times 17 {1 \over 3} = s$$

Simplify: $$s = 69 {1 \over 3}$$

Apr 13, 2022
#2
+115
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I had to go eat So that why you got here first  other wise

Kakashi  Apr 13, 2022
#3
+2541
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Sorry, this site is too addicting...

Also, it's not about getting here "first"... It's about helping people learn.

BuilderBoi  Apr 13, 2022
edited by BuilderBoi  Apr 13, 2022
#4
+115
-2

Ik i just love helping

Apr 13, 2022