Two Linear problem problems

Question

Question 1. A grant of $12,000 is said to be divided into 3 scholarships. How much is given to each scholarship if the second is double the first and the third is $1700 more than the second? 

 

 

Question 2. A man had $185 in five and ten dollar bills. How many of each did he have if he had 7 fives more than tens?

Answer 1

1.      Let x = 1st scholarship

             2x = 2nd scholarship

 2x + $1700 = 3rd scholarship

 

               x + 2x + (2x + 1700) = $12000

              5x + 1700 = 12000

              5x = 12000 - 1700

              5x = 10300

           5x/5 = 10300/5

 

                x = 2060

 

 

   Then, the 1st scholarship is worth $2060

                  2nd is double the first, so 2x = $4120

                  3rd is 2x + $1700 = 2(2060) + 1700 =4120 + 1700 = $5820

 

 

2.   Let x = number of $5 bills

           y = number of $10 bills

 

                     x - y = 7

                  5x + 10y = $185

 

Use elimination method. Multiply the first equation to -5

 

(x - y = 7) -5   -------->   -5x + 5y = -35
5x + 10y = $185  ----->   5x + 10y = $185    Add the two equations

 

 

                          TOTAL : 0 + 15y = 150

                                             15y = 150

                                          15y/15 = 150/15

                                               y = 10

     x - y = 7

     x -10 = 7

     x = 10 + 7

     x = 17

 

Therefore, there are 17 five dollar bills and 10 ten dollar bills