SOLUTION: Miranda has 6 more $5 bills than $10 bills. Altogether she has $135. How many of each bill does she have?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Miranda has 6 more $5 bills than $10 bills. Altogether she has $135. How many of each bill does she have?      Log On


   

Question 1130368: Miranda has 6 more $5 bills than $10 bills. Altogether she has $135. How many of each bill does she have?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
x of $10's
x+6 of $5's

5%28x%2B6%29%2B10x=135
--
5x%2B30%2B10x=135
15x=105
x=7

13 of $5
7 of $10

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, solve it using logical reasoning.

(1) Count the 6 "extra" $5 bills. That's $30, leaving $105, which now consists of equal numbers of $5 and $10 bills.
(2) One $5 bill and one $10 bill makes $15.
(3) The number of $5 and $10 bills needed to make the remaining $105 is 105/15 = 7.
(4) So, now counting all the bills, there are 7 $10 bills and 7+6 = 13 $5 bills.