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Homework Help: Algebra
Posted by Kristen on Tuesday, May 5, 2015 at 7:53pm.
A bank teller counts her $10 and $5 bills at the end of the day. She has a total of 70 bills. 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 am stuck about what to do next. Please help!
Reiny, thanks! I understand the difference between 5f and 5=f now - makes more sense! I forgot something from my original post, though...I forgot to include that she has 70 bills so I am reposting. THANKS!!!
ok, then you know f + t = 70
or t = 70-f
recall that the equation said:
5f + 10t = 595, which we reduced to
f + 2t = 119
replace t with 70-f
f + 2(70-f) = 119
f + 140 - 2f = 119
-f = -21
f = 21
so she has 21 fives.
Can you take it from there ?
If f = 21, the value has to be $105 and if there are 70 bills and 21 are 5's that means 49 are 10's which is $490. $490 + $105 = $595! 😄
Thanks...this kind of stuff is hard for me.
To write an equation that represents the total value of the money, you need to consider the value of each bill and the number of bills.
Let's assume that the number of $10 bills is d.
Since the bank teller has a total of 70 bills, we can write an equation:
d + f = 70
The value of each $10 bill is 10, so the total value of the $10 bills is 10d.
Similarly, the value of each $5 bill is 5, so the total value of the $5 bills is 5f.
The total value of the money is given as $595, so we can write another equation:
10d + 5f = 595
Now you have a system of equations:
d + f = 70
10d + 5f = 595
You can solve this system of equations using various methods such as substitution, elimination, or graphing to find the values of d and f.