# Find two numbers such that their sum equalls 21, and the greater number is 3 more than twice the smaller.

hala718 | Certified Educator

Assume that the smaller number is X and the greater number is y:

==> x+ y= 21.....(1)

We know that the greater number (y) is 3 more twice the smaller (x)

==> y= 3 + 2x ...(2)

Now substitute (2) in (1):

==> x+ y = 21

==> 3 + 2x + x= 21

==> 3+ 3x = 21

==> 3x = 18

==> x= 6

==> y= 3+2x

= 3+ 2(6)

= 3+ 12

= 15

==> y= 15

To check:

x+y= 21

6+15= 21

21=21

Also:

y= 3+2x

15= 3+ 2(6)

15= 3+ 12

15= 15

pohnpei397 | Certified Educator

x + y = 21.

x = 2y + 3

Now we solve using these two equations.

All we have to do is substitute the value for x that is giving in the second equation into the first equation.  Now we have

2y + 3 + y = 21

3y + 3 = 21

3y = 18

y = 6

If y = 6, then x must = 15.

We can check this by seeing if 15 is 3 more than twice 6.

(6*2) + 3 = 15

12 + 3 = 15

This is true so our values are correct.

lit24 | Student

Let the smaller number be x and the greater number be y.

So, x + y = 21

Next,

y = 3 + 2x

substituting 3 + 2x in the first equation for y we get

x + 3 + 2x = 21

3x = 21 - 3

3x = 18

x = 6

so

x + y = 21

6 + y = 21

y = 21 - 6

y = 15

Answer = the numbers are 6 and 15

giorgiana1976 | Student

Let's note the numbers a and b. From the enunciation we know:

- The sum of the numbers equalls 21:

a+b=21 (1)

- The greater number is 3 more than twice the smaller, when b is the greater number:

b = 2a+3 (2)

We'll re-write the relation (1):

a + 2a + 3 = 21

3a + 3 = 21

We'll factorize:

3(a+1) = 21

We'll divide by 3:

a+1 = 7

a+1-1 = 7-1

a = 6

b = 2a+3

b = 2*6 + 3

b = 15

So, the numbers are:

a = 6 and b = 15.

neela | Student

Though it is popular to use the algebraic methods we use the common man's way.

The greater number is 2times the smaller number and 3 more.

The greater and smaller number together 3 times and 3 which is  21.

So 21-3 is 3 times the smaller.

18 is 3 times the smaller. This implies the smaller is one third of 18. So the smaller is 6. And the greater is 2*6+3 = 15. Check 6 and 15 adds up to 21.

krishna-agrawala | Student

Let the smaller of the two number be x.

Then as per the given conditions that greater is three more than smaller number, the greater number:

= 2x + 3

Also as sum of the two numbers is equal to 21:

x + (2x + 3) = 21

==> 3x + 3 = 21

==> 3x = 21 - 3 = 18

Therefore:

x = 18/3 = 6

And

2x + 3 = 2*6 + 3 = 12 + 3 = 15