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Create a system of equations. Let x be the least number and y be the greatest number.
C
We are given that the sum of three numbers is 180 and two of them are the same. Let's call each of them x. Additionally, we know that each of x is 13 of the greatest number, which we can call y. Using this information we can write a system of equations.
2 x+ y=180 & (I) x=13 y & (II)
Let's solve this system using the Substitution Method. To do this, we will substitute 13y for x into the first equation.
(I):x= 13
(I):a*b/c= a* b/c
(I):a = 3* a/3
(I):Add fractions
(I):LHS * 3/5=RHS* 3/5
(I):a/b* b/a=1
(I):a/c* b = a* b/c
(I):a/b=.a /5./.b /5.
(I):Multiply
The greatest number is 108. To find the least number, we will substitute 108 for y in the second equation and evaluate.
(II):y= 108
(II):a/c* b = a* b/c
(II):a/b=.a /3./.b /3.
(II):a * 1=a
(II):a/1=a
The least number is 36. This corresponds with answer C.