The sum of three numbers is 16. The sum of twice the first number, 5 times the second number, and 6 times the third number is 85. The difference between 4 times the first number and the second number is negative 3. Find the three numbers.

1, 7, 8

Step-by-step explanation:

x, y, z - numbers to find

The difference between 4 times the first number and the second number is negative 3:

4x - y = - 3

- y = - 3 - 4x

y = 3 + 4x

The sum of three numbers is 16:

x + y + z = 16

x + 4x + 3 + z = 16

5x + z = 13

z = 13 - 5x

The sum of twice the first number, 5 times the second number, and 6 times the third number is 85:

2x + 5y + 6z = 85

2x + 5 (3 + 4x) + 6 (13-5x) = 85

2x + 15 + 20x + 78 - 30x = 85

-8x + 93 = 85

-8x = - 8

x = 1

y = 3 + 4•1 = 7

z = 13 - 5•1 = 8

Veryfying:

1 + 7 + 8 = 16

2•1 + 5•7 + 6•8 = 2 + 35 + 48 = 85