SOLUTION: the sum of three numbers is 10. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 47. The difference between 7 times the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the sum of three numbers is 10. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 47. The difference between 7 times the       Log On


   

Question 1088912: the sum of three numbers is 10. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 47. The difference between 7 times the first number and the second number is 20. Find the three numbers.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.A%2BB%2BC=10
2.2A%2B5B%2B6C=47
3.7A-B=20
From eq. 3,
B=7A-20
Substitute into eq. 1 and eq. 2,
A%2B%287A-20%29%2BC=10
4.8A%2BC=30
.
.
2A%2B5%287A-20%29%2B6C=47
2A%2B35A-100%2B6C=47
5.37A%2B6C=147
Multiply eq. 4 by 6 and subtract from eq. 5,
37A%2B6C-48A-6C=147-180
-11A=-33
Solve for A, then work backwards to solve for B and C.