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Nora and Renata had an equal number of polished stones at first. After Nora received 65 more stones and Renata lost 23 stones, Nora had three times as many stones as Renata. How many stones did they have altogether at first?

 Sep 16, 2021
 #1
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Let the number of polished stones that Nora and Renata had =N =R

 

N == R

 

R + 65==3 [R - 23]

R + 65==3R - 69

3R - R ==69 + 65

2R ==134

R == 134  polished stones they started with, or 134/2==67 stones each

 Sep 16, 2021
 #2
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n = r
(n+65) = 3 (r -23)
n + 65 = 3 (n-23)
n + 65 = 3 n - 69
134 = 2 n
n = r = 67
so
n + r = 134

 Sep 16, 2021
 #3
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Let's say they have altogether x at first

 

x/2 + 65 = (x/2 - 23) * 3

 

 x + 130 = 3x - 6x * 3

 

 268 = 2x

   x = 134

 

 smiley

 Sep 16, 2021

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