Question

if 16 is subtracted from twice the greater of two positive numbers, the result is half theother number. if 1 is subtracted from half the greater number, the result is still half theother number. find the two numbers.

Answer 1

The two positive numbers are determined by setting up a system of equations based on the given conditions and solving it step-by-step. The greater number is found to be 10 and the other number is 8.

Step-by-step explanation:

To solve the problem involving two positive numbers, let's call the greater number x and the other number y.

According to the first condition given, 2x - 16 = ½y. From the second condition, we have that ½x - 1 = ½y. To find the two numbers, we need to solve this system of equations:

1. Multiply the second equation by 2 to get rid of the fraction: x - 2 = y.
2. Substitute x - 2 in place of y in the first equation: 2x - 16 = ½(x - 2).
3. Multiply both sides of the equation by 2 to eliminate the fraction: 4x - 32 = x - 2.
4. Subtract x from both sides: 3x - 32 = -2.
5. Add 32 to both sides: 3x = 30.
6. Divide by 3 to find x: x = 10.
7. Substitute the value of x back into x - 2 = y to find y: 10 - 2 = y, therefore y = 8.

Hence, the two numbers the student is looking for are 10 and 8.