Question

What are the three integers whose sum is 137, given that the second number is 4 more than two times the first number, and the third number is 5 less than three times the first number?

A) 35, 48, 54
B) 40, 52, 45
C) 45, 52, 40
D) 48, 35, 54

Answer 1

To find the three integers, we define the first as x, and express the second and third in terms of x (2x + 4 and 3x - 5, respectively). Solving the equation x + (2x + 4) + (3x - 5) = 137 gives us x = 23, and substituting x back in gives us the three integers: 23, 50, and 64, which do not match any of the answer choices provided.

Step-by-step explanation:

The question asks to find three integers whose sum is 137 given certain relationships between the numbers. We can define the first integer as 'x' and express the second and third integers in terms of 'x'. The second integer is then '2x + 4' and the third integer is '3x - 5'. To find the value of 'x', we set up the equation:

x + (2x + 4) + (3x - 5) = 137

Solving for 'x' gives us:

x + 2x + 4 + 3x - 5 = 137

6x - 1 = 137

6x = 138

x = 23

Substituting 'x' back into the expressions for the other two numbers, we get the second number as '2(23) + 4 = 50' and the third number as '3(23) - 5 = 64'. The three integers are therefore 23, 50, and 64, which is not listed as an option, so it appears there might be an error in the provided choices. Therefore, the three integers whose sum is 137 are 23, 50, and 64.