The larger of two numbers is 6 more than 4 times the smaller. If the smaller number is one-fifth of the larger, find both numbers.

Question

The larger of two numbers is 6 more than 4 times the smaller. If the smaller number is one-fifth of the larger, find both numbers.

Need halp plz

Answer 1

First, we assign variables for the numbers we want to find.

 

Let the smaller number = x

Let the larger number = y

 

Next, we write equations that describe the situation using these variables.

 

y = 4x + 6                eq1

x = y/5                     eq2

 

We have two equations.  We cannot solve each equation individual since they have two unlike variables, x and y.  We can substitute one equation into another, so that we have only one equation with one variable to deal with.

 

 

Let's substitute  eq2 into eq1.  This will get eq1 in terms of y.

 

y = 4(y/5) + 6

 

y = (4/5)y + 6

 

(1/5)y = 6

 

y = 30

 

 

Now substitute this value of y into eq2 to solve for x.

 

x = 30 / 5

x = 6

 

 

The smaller number is 6.

The larger number is 30.