SOLUTION: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the

Question 159625: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers.
:
Let x = "the first number"
Let y = "the second number"
Let z = "the third number"
:
Write an equation for each statement:
:
'The second of three numbers is 7 less than 3 times the first."
y = 3x - 7
:
" The third is 13 less than 6 times the first."
z = 6x - 13
:
"If twice the first is decreased by the third, the result is -3."
2x - z = -3
:
Find the three numbers.
:
Note that the 2nd equation is: z = (6x-13), substitute this for z in the last equation:
2x - (6x-13) = -3
2x - 6x + 13 = -3; (removing the brackets, changes the sign of 13)
2x - 6x = -3 - 13
-4x = -16
x =
x = +4
:
Recall that z = 6x -13, substitute 4 for x
z = 6(4) - 13
z = 24 - 13
z = 11
and
y = 3x - 7; substitute 4 for x again
y = 3(4) - 7
y = 12 - 7
y = 5
:
:
Check our solution in the statement:
" If twice the first is decreased by the third, the result is -3.
2(4) - 11 = -3
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