Susan saved $345 in $5,$10 and $50 notes. There were 35 notes altogether. She had 4 more $10 notes than $50 notes. How many $5 notes did she have?

Question

I do not know the formula.

it is difficult.

Answer 1

Let x = #5's, y = #10's, z = #50's

 

x + y + z = 35 total number of notes - call this (1)

 

5x + 10y + 50z = 345 total value of all the notes

5x +  5y  + 5z   = 175  (I multiplied (1) by 5)

         5y  + 45z = 170  subtracted the 2 equations here

          y   +  9z  = 34  divided the above equation by 5 - call this (2)

                     y  = z + 4 because there are 4 more 10's than 50's

substitute into (2)

         z + 4 + 9z = 34

                    10z = 30, so z = 3

                   so y = 3 + 4 =7

                so x    = 35 - (3 + 7) from (1), so x = 25

 

so there are 25 $5 notes.