SOLUTION: the sum of three numbers is 15. The second number is two less than the first number. The sum of the first two numbers is twice the third number. Identify the three numbers.
Question 1184033: the sum of three numbers is 15. The second number is two less than the first number. The sum of the first two numbers is twice the third number. Identify the three numbers. Found 3 solutions by ankor@dixie-net.com, josgarithmetic, greenestamps:Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website! Sum of three numbers is 15.
a + b + c = 15
The second number is two less than the first number.
b = a - 2
or we can rearrange and write it
a - b = 2
The sum of the first two numbers is twice the third number.
a + b = 2c
Identify the three numbers.
:
Notice a + b is in 1st and 3rd equation, so in the 1st equation we can write it
2c + c = 15
3c = 15
c = 15/3
c = 5
In the 1st equation, replace c with 5
a + b + 5 = 15
a + b = 15 - 5
a + b = 10
Use elimination with rearranged equation
a + b = 10
a - b = 2
-----------addition eliminates b, find a
2a + 0 = 12
a = 12/2
a = 6
find b
6 + b = 10
b = 10 - 6
b = 4
:
:
Check: 6 + 4 + 5 = 15 Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
NUMBERS DESCRIPTION
x x
y x-2
z
SUM 15
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Revising the table,
NUMBERS DESCRIPTION
x x
y x-2
z x-1
SUM 15
There are dozens of ways to set up this problem for solving....
I would do some logical analysis on the given information to make the required algebra easier. In fact my preference would be to solve the whole problem without formal algebra.
(1) Since the sum of the first two numbers is twice the third number, the third number is one-third of the total.
(2) Then, since the sum of the three numbers is 15, the third number is 15/3=5.
(3) Then the sum of the first two numbers is 15-5=10.
(4) Then, since the second number is 2 less than the first, the first number is 6 and the second is 4.
ANSWER: 4, 5, and 6
If an algebraic solution is required, I would still do the logical analysis of (1) and (2) above to determine that the third number is 5. Then
let x = first number
then x-2=second number
The sum of the three numbers is 15:
The first two numbers are x=6 and x-2=4; the three numbers are 4, 5, and 6.