Solve applications

Question

The difference between two numbers is 9. Two times the larger number is 4 times the smaller number. Write a system of equations describing the given conditions. Then solve the system by the substitution method and find the two numbers.

Answer 1

Let x be the larger number and y be the smaller one.

• The difference between the two numbers is 9:  x - y = 9
• Two times the larger number (2x) is (=) 4 times the smaller number (4y):  2x = 4y

 

x - y = 9

2x = 4y

 

Since x - y = 9, x = 9+y.  Substitute 9+y in place of x in the second equation:

 

2x = 4y

2(9+y) = 4y

 

Solve for y.  Once you've found the value of y, use x = 9+y to find x.