SOLUTION: Please show me the steps on how to solve this. Thanks. The sum of three numbers is 140. The smallest number is 10 less than the middle number; the largest number is three times th

Question 1082976: Please show me the steps on how to solve this. Thanks.
The sum of three numbers is 140. The smallest number is 10 less than the middle number; the largest number is three times the smallest number. What is the largest number of the three?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a be the smallest number.
let b be the middle number.
let c be the largest number.

the smallest number is 10 less than the middle number.
this gets you a = b-10

the biggest number is 3 times the smallest number.
this gets you c = 3a

in the equation of c = 3a, solve for a to get a = c/3

since a = b - 10 and a = c/3, then b - 10 = c/3

solve for c to get c = 3b - 30

you now have:

a = b - 10
c = 3b - 30

a + b + c = 140 becomes b - 10 + b + 3b - 30 = 140, after you replace a with b - 10 and c with 3b - 30

combine like terms to get 5b - 40 = 140

add 40 to both sides to get 5b = 180

divide both sides by 5 to get b = 36

a = b - 10 gets you a = 26

c = 3b - 30 gets you c = 78

a + b + c becomes 26 + 36 + 78 = 140.

a = b - 10 gets you 26 = 36 - 10 which becomes 26 = 26

78 = 3b - 30 gets you 78 = 108 - 30 which becomes 78 = 78

everything checks out ok so the solution is good.

the solution is that the largest number of the three is equal to 78.

you could also have used c = 3a to get 78 = 3*26 = 78 to confirm the numbers are good.

in fact, you should always use the original equations to confirm the numbers are good and c = 3a was the original equation.

c = 3b - 30 was a derived equation based on the original equations.

while it also confirmed the solution was correct, it was not an original equation and could have been wrong, in which case the confirmation could have been wrong.

but, all was well and your solution is that the largest number of the three is 78.

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