Known information:
- the sum of three numbers: 24
- the smallest number is 2 less than the largest number
- the largest number is equal to the sum of the smallest and middle number.
Let us set up some variables for our terms:
- smallest number --> S
- middle number --> M
- largest number -- L
Let us set up some equations in terms of our known information
- S + M + L = 24
- S = L - 2
- L = S + M
Let us set up everything in terms of L, because in the first equation, we will be able to get rid of all the other variables but L allowing us to solve the equation:
(S + M) + L = 24 ---> L + L = 24
2L = 24
L = 12
Since L = 12, we know that S = L - 2:
S = L - 2 = 12 - 2 = 10
Since now we know that L = 12, and S = 10, and L = S + M:
L = S + M
12 = 10 + M
M = 2
So our answer is 2, 10, 12
Hope that helps!