Question

The sum of three numbers 13. The sum of twice the first number, five times the second number, and six times the third number is 60. The difference between four times the first number and the second number is 14. Find three numbers.

Answer 1

Answer:

The three numbers are 56/5, -39/5 and 78/5.

Step-by-step explanation:

EQUATION 1:

First number: x

Second number: y

Third number: z

x + y + z = 19

EQUATION 2:

Sum of following is 77

Twice the first number: 2x

5 times the second number: 5y

6 times the third number: 6z

So, 2x + 5y + 6z = 77

EQUATION 3:

Difference between first and second number is 19.

x - y = 19

Equation 1: x + y + z = 19

Equation 2: 2x + 5y + 6z = 77

Equation 3: x - y = 19

1. Find x in terms of y

x - y = 19

x = 19 + y

2. Find y in terms of z by putting the value of x in first and second equation

  x + y + z = 19

  (19 + y)+ y + z = 19

  2y + z = 19 - 19

  2y + z = 0

  y = -z/2

and

2(19+y)+5y+6z=77

now putting the value of y in this equation

2(19-z/2)+5(-z/2)+6z=77

38 - z -5z/2 +6z = 77

5z/2 + 38 = 77

5z/2 = 39

z = 78/5

Now, y = -z/2

y = (-78/5)/2

y = -39/5

and  x = 19 + y

x = 19 - 39/5

x = 56/5

Therefore, the three numbers are 56/5, -39/5 and 78/5.

Keyword: Sum

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Answer 2

1567.







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