word problem

Question

The sum of two numbers is 30. The first number is 1/2 of the second number. What are the numbers? What is the smaller of the two numbers? What is the larger of the two numbers?

Answer 1

Let the two numbers be x and y

x + y = 30

x = 0.5y

 

Substitute 2nd equation into 1st

0.5y + y = 30

1.5y = 30

y = 30/1.5 = 20 (Larger)

x = 0.5*(20) = 10 (Smaller)

 

 

Answer 2

Here's what we know:

a + b = 30

a = b/2

 

Since we have a value for a, we can put that into our equation:

b/2 + b = 30

3b / 2 = 30

Divide both sides by 3/2:

b = 2 * 30 / 3

b = 2 * 10

b = 20

 

Now to solve for a:

a = 20 / 2

a = 10

 

Now to check:

20 + 10 = 30

30 = 30