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 53. The difference between 7 times the

Algebra ->  Coordinate Systems and Linear Equations -> 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 53. The difference between 7 times the      Log On


   

Question 1124074: 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 53. The difference between 7 times the first number and the second number is 4.
Find the three numbers.
first​ number:

second​ number:

third​ number:


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let's three numbers be x, y, and z

if the sum of three numbers is 10, we have
x%2By%2Bz=10......eq.1

if the sum of twice the first number, 5 times the second number, and 6 times the third number is 53, we have

2x%2B5y%2B6z=53......eq.2

if the difference between 7 times the first number and the second number is 4,we have
7x-y=4........eq.3

solve eq.3 for y

y=7x-4.....eq.a.....substitute in eq.2

2x%2B5%287x-4%29%2B6z=53......eq.2
2x%2B35x-20%2B6z=53
37x%2B6z=53%2B20..........solve for z
6z=73-37x
z=73%2F6-37x%2F6......eq.b
substitute y and z from eq.a and eq.b in eq.1

x%2B7x-4%2B73%2F6-37x%2F6=10......eq.1
8x-37x%2F6=10%2B4-73%2F6
8x-37x%2F6=14-73%2F6...both sides multiply by 6
48x-37x=84-73
11x=11
highlight%28x=1%29

go to y=7x-4.....eq.a substitute x
y=7%2A1-4
highlight%28y=3%29

go to z=73%2F6-37x%2F6......eq.b substitute x
z=73%2F6-%2837%2A1%29%2F6
z=36%2F6
highlight%28z=6%29