Question

There are two numbers. The first number minus the second number is 15. One-third of the sum of the numbers is one quarter of the first number. What are the two numbers?

Answer 1

12 and -3

Explanation:

Let's assume the first number to be X And

The second number to be Y

First statement says that X - Y = 15_____ equation 1

And the second statement says that

1/3 × (X + Y) = (1/4 × X)

Open up the above bracket and expand the equation and we have

4x + 4y = 3x

X + 4Y = 0_______equation 2

From equation 1 which is x - y = 15,

Make X the subject of the formula and replace in equation 2

X = 15 + y

Replace the above in equation 2

(Which is X + 4Y = 0)

15 + y + 4y = 0

15 + 5y = 0

Y = -3

Now substitute Y = -3 in equation 1 above

X - Y = 15

X-(-3) = 15

X + 3 = 15

X = 12.

Both numbers are therefore, 12 and -3 respectively

Answer 2

So the numbers are 12 and -3.

Explanation:

In order to solve this problem we will attribute variables to the numbers, the first one will be "x" and the second one will be "y". From the first sentence we know that the subtraction of the two numbers is equal to 15, so we have:

x - y = 15

Then the problem states that one-third of the sum of the number is equal to one quarter of the first number, so we have:

(1/3)*(x+y) = x/4

Since we now have two equations and two variables we can solve for x and y. From the first equation we have:

y = x - 15

Using this expression for the value of y in the second equation:

(1/3)*(x + x - 15) = x/4

(1/3)*(2*x - 15) = x/4

2*x - 15 = 3*x/4

2*x - 3*x/4 = 15

(8*x - 3*x)/4 = 15

5*x/4 = 15

5*x = 60

x = 60/5 = 12

y = x - 15 = 12 - 15 = -3

So the numbers are 12 and -3.