Application problems- More than one unkown

Question

The larger of two numbers is 15 less than four times the smaller number. The sum of the two numbers is 65. Find the two numbers,

What are the numbers?(Use a comma to separate answers as needed)

Answer 1

HI Michael, 

 

Start by declaring values for both the larger number and the small number:

 

Let the small number = x; Let the large number =y.

 

The text tells us that "The larger of two numbers is 15 less than four times the smaller number".  This is illustrated by:

 

y=4x-15

 

Similarly, the text tells us that "The sum of the two numbers is 65".  This is illustrated by:

 

x+y=65

 

Solve the second equation for x so that we can substitute it into the first equation:

 

x+y=65 --> x=65-y

 

Substituting this into the first equation we get, 

 

y=4(65-y)-15

y=260-4y-15

**add 4y to each side

5y=260-15

**add the constants on the right side

5y=245

**divide each side by 5

y=49

 

Substitute your value for Y into x+y=65 to get

 

x + 49=65

**subtract 49 from each side

x=16

 

Thus, the smaller number is 16 and the larger number is 49

 

Answer 2

Let x = the smaller number, y = larger number.  We know

 

y = 4x - 15 and 

 

x + y = 65

 

Substitute for y in the 2nd equation and solve for x

 

x + (4x - 15) = 65

5x = 80

x = 16

 

so y = 4*16 - 15 = 49

 

So the 2 numbers are 49, 16