The larger of two numbers is twelve more than twice the smaller number. The sum of the numbers is fifty one. Find each number

Answer: 13 and 38

Step-by-step explanation:

Let the smaller number be y.

Larger number will be 2y+12

Since the sum of the numbers is 51,

y + 2y + 12 = 51

3y + 12 = 51

3y = 51 - 12

3y = 39

y = 39/3

y = 13

The smaller number is 13

The bigger number will be 2y + 12 = 2 (13) + 12 = 26 + 12 = 38

13 and 38

Step-by-step explanation:

So we know that one number is 2 times the smaller number plus 12. We can use the variable x for the smaller number and the bigger number will be 2x + 12. Now we need to put the numbers into an equation.

2x + 12 + x = 51

To isolate x, we have to subtract 12 from the left side of the equation.

2x + x = 39

Now we add the x's together.

3x = 39

Now we have to divide by 3.

x = 13

But we're not done yet, although we know the smaller number is 13 we have to plug x into the larger number. So because it is 2x the amount, we multiply 13 to get 26 and then add another 12 to get 38.