A bank teller counts her $10 and $5 bills at the end of the day. The total value of the money is $595. Let f represent the number of $5 bills.
I have to write an equation that represents the total value of the money. I know f = 5 and 2f = 10 but I am stuck about what do do next. Please help!
f stands for the number of $5 bills, so by saying f = 5, you are saying there are five $5 bills.
It does not say that anywhere
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let f be the number of fives
let t be the number of tens
so the VALUE of our fives = 5f
and the VALUE of our tens = 10t
5f + 10t = 595
divide by 5
f + 2t = 119
Reiny, thanks! I understand the difference between 5f and 5=f now - makes more sense! I forgot something from my original problem, though...it also says the bank teller has a total of 70 bills. Now what?!
To represent the total value of the money, we need to calculate the value of $10 bills and $5 bills separately and then add them together.
Let's use the given information: f represents the number of $5 bills, so we know that the value of the $5 bills is $5 multiplied by f which gives us 5f.
Similarly, we can represent the value of the $10 bills as follows: Since each $10 bill is twice the value of a $5 bill, we have 2f $10 bills. Therefore, the value of the $10 bills is $10 multiplied by 2f which gives us 20f.
Now, we can write the equation representing the total value of the money:
Total value = Value of $10 bills + Value of $5 bills
Total value = 20f + 5f
Since the total value of the money is given as $595, we can set up the equation as follows:
595 = 20f + 5f
Now you can solve this equation to find the value of f. Combine like terms on the right side of the equation:
595 = 25f
Next, isolate f by dividing both sides of the equation by 25:
f = 595 / 25
Simplifying the expression:
f = 23.8
Since f represents the number of $5 bills, we need to have a whole number of bills, so we cannot have 0.8 of a bill. Therefore, we can assume that f = 24.
So, there are 24 $5 bills.
You can then substitute the value of f back into the equation to find the value of the $10 bills:
Value of $10 bills = 2f = 2 * 24 = 48
Hence, there are 48 $10 bills.
Therefore, the equation representing the total value of the money is 595 = 48 * 10 + 24 *5.