Question

the sum of two numbers is 30. the larger number is two more than three times the smaller number. what are the numbers?

Answer 1

The numbers are 23 and 7.

Explanation:

x+y=30

x>y

x=3y+2

3y+2+y=30

4y+2=30

4y=30-2

4y=28

y=28/4

y=7

----------------

x=3(7)+2=21+2=23

Answer 2

Answer: 7 and 23

Explanation:

Let the first number be x and the second number be y.

From the first statement , we have

x + y = 30 --------------- equation 1

Taking x as the larger number , from the second statement , we have

x = 3y + 2 --------------- equation 2

substitute equation 2 into equation 1 , we have

3y + 2 + y = 30

4y + 2 = 30

4y = 28

y = 7

substitute y = 7 into equation 2 , we have

x = 3(7) + 2

x = 21 + 2

x = 23

therefore : x = 23 and y = 7