Question

three times a number is subtracted from another number and the difference is 3. The sum of the two numbers is 31. What is the smaller of the two numbers

Answer 1

ANSWER

The smaller number is 7.

EXPLANATION

Let the numbers be x and y.

Then we have;

y-3x=3... eqn (1)

If the sum of the numbers is 3 then,

y+x=31... eqn (2)

Eqn(2) - Eqn (1)

x--3x=31-3

$4x = 28$

Divide both sides by 4,

$x = 7$

We put x=7 into the second equation,

y+7=31

y=31-7

y=24

The smaller of the two numbers is 7.

Answer 2

Answer:  The two numbers are 7 and 24. The smaller of the two numbers is 7

Step-by-step explanation:

Let the two numbers be x and y

The mathematical interpretation of the first statement  (three times a number is subtracted from another number and the difference is 3)   is  y - 3x = 3

For the second statement ( the sum of the two numbers  is 31), its mathematical interpretation is x+ y = 31

from y  = 31  - x

       we can substitute y in the equation y - 3x = 3

(31 - x)   -  3x   =  3

Then we can now proceed and solve for x

31 - x -3x  = 3

31 - 4x   =  3          subtract 31  from both-side of the equation

31 - 31 - 4x = 3 - 31

-4x   =    -28

Divide both-side of the equation by -4

$\frac{-4x}{-4} = \frac{-28}{-4}$

x    =    7

substituting x = 7 in    y =  31 - x

y  =   31 -  7  =   24

x= 7     and y = 24

The two numbers are 7 and 24

Therefore the smaller number is 7