Algebra word problem

Question

Two  numbers have a sum of 65 . Four times the smaller number is equal to 10 more than the larger number. Find the numbers .

Answer 1

For this problem,  there are two unknown numbers so we will try to form two equations to solve for the variables.  We can let the larger number = x, and the smaller number = y .  The first thing we are told is two numbers sum to 65, so we can say the   x + y = 65 (equation 1).   Next we are told that 4 times the smaller is equal 10 more than the larger,  so when we translate this we get  4*y = x + 10 (equation 2).  To solve this, we want to solve for one of the variables in equation 1 and plug this result into equation 2 to solve for the variable.  Once we have the value of one variable we can fine the second by plugging in the solved variable into one of the 2 equations. 

 

If,  x = 65 - y  ---->  4*y = 65 - y + 10        Then,         x = 65 - y 

                                    +y         +y                                   x = 65 - 15

                                                                                         x = 50

                                  5*y = 75

                                 ÷5     ÷5

 

                                      y = 15

 

 

 

Answer 2

x +  4x+10 = 65

 

5x + 10 = 65

 

5x = 55

 

x=11

 

 

11 and 4(11)+10 = 44 + 10 = 54