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

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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

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.

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**

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

We'll add -1 both sides:

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.**

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.

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

Answer:

The two numbers are 6 and 15.