Question 93172: A bill of $123 was paid with $5 and $1 coins, a total of 59 notes being used. how many $5 notes were used?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let F represent the number of $5 notes and let S represent the number of $1 notes.
.
Since the total number of notes used is 59, you can write an equation for the total as:
.
F + S = 59 <==== equation 1
.
Since the total monetary value of the $5 notes is $5 times F and the total monetary
value of the $1 notes is $1 times S you can add these two monetary values and set the sum
equal to the $123 bill. In equation form this is:
.
5*F + 1*S = 123 <====equation 2
.
These two equations can be solved as a set. One way to do this is to go to equation 1
and solve it for one variable in terms of the other. For example, if you subtract F
from both sides of equation 1 the result is:
.
S = 59 - F
.
Next you can use that result to modify equation 2. Since S and 59 - F are equal, in equation 2
you can replace S with the quantity (59 - F). When you do that equation 2 becomes:
.
5*F + 1*(59 - F) = 123
.
This simplifies to:
.
5F + 59 - F = 123
.
On the left side, you can combine the 5F and -F to get 4F. This simplifies the equation into:
.
4F + 59 = 123
.
Next you can get rid of the 59 on the left side by subtracting 59 from both sides of the
equation. This results in:
.
4F = 64
.
Finally you can solve for F by dividing both sides by 4 to get:
.
F = 64/4 = 16
.
Since F represents the number of $5 notes, you now know there are 15 $5 notes.
.
If there are 16 each of the $5 notes and the total number of notes is 59, that means that
there must be 59 - 16 or 43 each of the $1 notes.
.
You can check that out to make sure the result is enough to pay the $123 bill. If you count
out 16 of the $5 notes you get $80 ... 16 times $5 = $80. Then you add to that amount
43 of the $1 notes and the total is $80 + $43 = $123. That works! So your answer is correct
and the answer to the problem is that there are 16 of the $5 notes used in paying the
bill.
.
Hope this helps you to understand the problem.
|
|
|
