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 numbers?

Answer:

First number: 12

Second number: -3

Step-by-step explanation:

First, let's establish some variables:

x= first number

y= second number

Now, let's turn what is told to us into equations:

The first number minus the second number is 15

  x - y = 15

One-third of the sum of the numbers is one quarter of the first number

 1/3 ( x + y ) = 1/4 ( x )

Now, let's use the first equation given to us to find x in terms of y:

x - y = 15     [Add y to both sides]

x = y + 15

Next, we will take the value of x we found and plug it into the second equation:

1/3 ( x + y ) = 1/4 ( x )     [Plug in x]

1/3 ( {y + 15} + y ) = 1/4 ( {y + 15} )     [Combine like terms]

1/3 ( 2y + 15 ) = 1/4 ( {y + 15} )     [Distribute on both sides]

(2/3)y + 5 = (1/4)y + 15/4     [Subtract 15/4 from both sides]

(2/3)y + (5/4) = (1/4)y     [Subtract (2/3)y from both sides]

5/4 = (-5/12)y     [Multiply both sides by -12/5]

-3 = y

Since we have now found the value of y, let's plug it into our first equation to find the value of x:

x - y = 15     [Plug in y]

x - (-3) = 15     [Simplify]

x + 3 = 15     [Subtract 3 from both sides]

x = 12

So, our first number must be 12 while our second number is -3.

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Answer:

-12 and 3

Step-by-step explanation:

Let first no. be x

First number - Second number = 15

So, x - 2nd no. = 15

Second number = 15 + x

First number = x

Now, One-third of the sum of numbers is = [tex]\frac{x+(15+x)}{3} = \frac{15+2x}{3}[/tex]

One-quarter of first number = [tex]\frac{x}{4}[/tex]

Now,

[tex]\frac{15+2x}{3} = \frac{x}{4}[/tex]

= 4(15+2x) = 3x

= 60 + 8x = 3x

= 60 = -5x

= -12 = x

Hence, First number = -12

Second number = -12 + 15 = 3

Check:

[tex]\frac{15-24}{3} = \frac{-12}{4}[/tex]

= [tex]\frac{-9}{3} = -3[/tex]

= -3 = -3

Hence, proved!

Hope it helped. Pls mark me the BRAINLIEST!

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