The sum of three numbers is 45 one number is 10 more than the second number it is also twice the third number find the numbers

X = 1st number, y = 2nd number, z = 3rd number

x + y + z = 45
x = y + 10x - 10 = y
x = 3z1/3x = z

x + x - 10 + 1/3x = 45
2 1/3x - 10 = 45
7/3x = 45 + 10
7/3x = 55
x = 55 / (7/3)
x = 55 * 3/7
x = 165/7

x - 10 = y
165/7 - 10 = y
165/7 - 70/7 = y
95/7 = y

1/3x = z
1/3(165/7) = z
165/21 = z
55/7 = z

check...
x + y + z = 45
165/7 + 95/7 + 55/7 = 45
315/7 = 45
45 = 45 (correct)

so, x = 165/7
    y = 95/7
    z = 55/7