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 + 10 ... x - 10 = y

x = 3z ... 1/3x = 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