Answer:
There are 106 $5 bills and 59 $20 bills.
Step-by-step explanation:
1. Let us call the number of $5 dollar bills x and the number of $20 bills y.
The problem states that the total value of the money was $1710. This means that the total value of the $5 and $20 bills together is $1710. We can write this as:
5x + 20y = 1710
We are also given that there were 47 more $5 bills than $20 bills. We can write this as:
x = y + 47
2. Thus, we have two simultaneous equations:
(1) 5x + 20y = 1710
(2) x = y + 47
3. Our aim is now to solve for x and y to find the number of each type of bill.
Now there are many different methods of solving from this point onwards, however I personally would substitute x = y + 47 into equation (1), simply because this method does not require any extra rearranging.
I would also simplify equation (1) before substituting to make calculations easier (especially in the case you are not using a calculator) - note however that this isn't compulsory and you would still get the same answer without simplification.
Thus, simplifying we get:
5x + 20y = 1710
x + 4y = 342 (Divide both sides by 5)
Now, substituting in x = y + 47, we get:
x + 4y = 342
(y + 47) + 4y = 342 (Substitute x for y + 47)
5y + 47 = 342 (y + 4y = 5y)
5y = 295 (Subtract 47 from both sides)
y = 59 (Divide both sides by 5)
Now that we know that y = 59, we can substitute this back into x = y + 47 to solve for x:
x = 59 + 47
x = 106
4. Thus, x = 106 and y = 59.
This means that there are 106 $5 bills and 59 $20 bills.
The key to this problem is to recognise the need to set up a set of simultaneous equations and then solve for the respective variables.
Hope that helped but if you have any further questions please feel free to comment below :)
