Question

he difference of 1/2 of one number and 2/3 of another number is equal to 2. If the first number were to decrease by 5/6 of it, and the second number were to increase by 1/6 of it, their sum would be equal to 59. Find the two numbers.

Answer 1

• the first number is 60
• the second number is 42

Explanation:

If we let x and y represent the first and second numbers, respectively, then the first sentence of the problem statement tells us ...

(1/2)x - (2/3)y = 2

The second sentence of the problem statement tells us ...

(1 -5/6)x +(1 +1/6)y = 59

Solution

Multiplying the first equation by 6 gives ...

3x -4y = 12

Multiplying the second equation by 6 gives ...

x + 7y = 354

Solving the second equation for x gives ...

x = 354 -7y

Substituting that into the first equation gives ...

3(354 -7y) -4y = 12

1050 = 25y . . . . . . . . subtract 12-25y

42 = y . . . . . . . . . . . . divide by 25

Then we can find x using its equation ...

x = 354 -7·42 = 60

The first number is 60; the second number is 42.