Four numbers have a sum of 165. The 1st number is 5 more than quadruple the 3rd. The 2nd number is 7 less than triple the 3rd. The 4th number is 14 more than half the 3rd. Find all four numbers.

Answer 1

3rd number: n

1st number: 4n + 5

2nd number: 3n - 7

4th number: (n/2) + 14

The sum of these equals 165. Can you solve for n and answer?

Answer 2

Hello, Dfgf5,

assign the letters a, b, c, and d to the four numbers. They add to 165

a+b+c+d=165

The 1st number is 5 more than quadruple the 3rd: a = 4c + 5

The 2nd number is 7 less than triple the 3rd: b = 3c - 7

The third number, c, is left totally undefined. It is the value that appears in all the other relationships, sp we'll focus on it when we start the solution.

The 4th number is 14 more than half the 3rd: d = 0.5c + 14

All the numbers make reference to c, so lwt'e start there and determine if we can find the value of c. Take the first equation and rearrange all the equations for a, b, c, and d, so that we can eliminate all unknowns except c.

a + b + c + d = 165

Substitute all the more detailed equations in the above equation to get:

4c + 5+ 3c - 7 + c + 0.5c + 14 = 165

Solve for C and then use that nto find a, b, and d

(77, 47, 18. 23)

Bob