SOLUTION: the sum of three numbers is 105. the third is 11 less than ten times the second. twice the first is 7 more than 3 times the second. find the numbers.

Question 476514: the sum of three numbers is 105. the third is 11 less than ten times the second. twice the first is 7 more than 3 times the second. find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of three numbers is 105.
x + y + z = 105
:
The third is 11 less than ten times the second.
z = 10y - 11
:
twice the first is 7 more than 3 times the second.
2x = 3y + 7
:
Multiply the 1st equation by 2
2x + 2y + 2z = 210
Replace 2x with (3y+7)
3y + 7 + 2y + 2z = 210
5y + 2z = 210 - 7
5y + 2z = 203
Replace z with (10y-11)
5y + 2(10y-11) = 203
5y + 20y - 22 = 203
25y = 203 + 22
25y = 225
y =
y = 9
:
z = 10(9) - 11
z = 79
:
2x = 3(9) + 7
2x = 34
x = 17
:
:
check this
17 + 9 + 79 = 105 confirms our solutions of x=17, y=9, z=79
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