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Ryan's bag contains 5 times as many coins as Gavin's bag. If Ryan gives 18 coins to Gavin, the two boys will have the same number of coins. What is the total number of coins?

 May 23, 2021
 #1
avatar+114485 
+1

Let Ryan have R coins and Gavin have G coins

 

Ryan's bag contains 5 times as many coins as Gavin's bag.       so       5G=R    (1)

 

If Ryan gives 18 coins to Gavin

that would mean that Ryan ends up with 18 less and Gavin will have 18 more than before,

then they will have the same amount.

so

R-18=G+18         (2)

 

Now you have 2 equations that must be solved simultaneously.   Can you take it from there Tg ?

 May 24, 2021
 #2
avatar+315 
+1

R = 37, G = 1

Tgfromthe4  May 24, 2021
edited by Tgfromthe4  May 24, 2021
edited by Tgfromthe4  May 24, 2021
 #3
avatar+114485 
+1

thanks for responding, unfortunately that is not correct because 5G does not equal R

 

lets see.  You have 2 equations that must be solved simultaneously.

 

5G=R

R=5G   (1)

 

and

 

R-18=G+18    (2)

 

 

 

so you have to replace R in the second equation with 5G  (this is called substitution method)

 

(2) becomes

 

5G -18= = G+18

 

Now solve it for G and then go back and solve for R

Melody  May 25, 2021
 #4
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+1

9 is the answer

Guest May 25, 2021
 #5
avatar+315 
+1

G = 9

 

R = 45

Tgfromthe4  May 25, 2021
 #6
avatar+114485 
+1

Excellent.

 

I would have liked to have seen some of your working.

If you just guessed, using trial and error, that will not always work for you.

 

You need to know how to solve simultaneous equations formally.

 

Anyway, you have the right answer so congratulations!   

And thanks for responding to my posts.    laugh

Melody  May 25, 2021

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