SOLUTION: The sum of three numbers is 32 the difference between the largest and the smallest number is 17. The sum of the two smaller numbers is 13 find the numbers

Question 420001: The sum of three numbers is 32 the difference between the largest and the smallest number is 17. The sum of the two smaller numbers is 13 find the numbers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three numbers, x, y, z (x is the smallest)
:
The sum of three numbers is 32
x + y + z = 32
:
the difference between the largest and the smallest number is 17.
z - x = 17
z = (x+17)
:
The sum of the two smaller numbers is 13
x + y = 13
y = (-x+13)
:
find the numbers
Replace z and y in the 1st equation
x + (-x+13) + (x+17) = 32
Combine like terms
x - x + x + 13 + 17 = 32
x + 30 = 32
x = 32 - 30
x = 2 is the smallest number
then
y = -2 + 13
y = 11
and
z = 2 + 17
z = 19 is the largest number
:
:
Check solutions
2 + 11 + 19 = 32
RELATED QUESTIONS
The sum of four even consecutive numbers is 100. What is the difference between the... (answered by luke94,MathTherapy)

The sum of three numbers is 44. The difference between the largest and the smallest is... (answered by checkley77)

The sum of three numbers is 40. The difference between the largest and smallest is 12,... (answered by Fombitz)

The sum of the numbers is 72. The difference between the largest and smallest is 32. The... (answered by advanced_Learner)

The ratio of three numbers is 2:3:7. If the sum of the numbers is 360, what is the... (answered by ikleyn)

The sum of three numbers is 17. Two times the smallest is 4 less than the largest, while... (answered by ramkikk66)

The sum of three numbers is 10 . Two times the smallest is 1 less than the largest,... (answered by CubeyThePenguin)

The sum of the digits of a 3 digit number is 8. The difference between the largest and... (answered by fcabanski)

the sum of three number is 55. the difference of the largest and the smallest is 51, and (answered by ikleyn)