Anna has 12 bills in her wallet, some $5 and some $10. The total value of the bills is $100. HOw many of each bill odes Anna have?
How do i solve these type of problems my quess was this but i don't know if i'm correct.
5(x) + 10(y) = 100
5(0) + 10y = 100
10y = 100
--- ---
10 10
y = 10
5(x) + 10(10) = 100
5x + 100 = 100
-100 -100
5x = 0
--- ---
5 5
x = 0
to check is :
5(0) + 10(10) = 100
0 + 100 = 100
100 = 100
you have the intercepts ok.
but its asking about how many of each so is my answer correct or what am i doing wrong.
5(x)+10(12-x)=100
5x+120-10x=100
-5x=-20
5x=20
x=4(no of 5dollar bills)
12-4=8(no of10dollar bills)
Your approach to solving the problem is correct, but there is a mistake in your calculations. Let's go through the problem step by step and correct it.
Let's define:
x = the number of $5 bills
y = the number of $10 bills
The total number of bills is given as 12. Therefore, we have our first equation:
x + y = 12
The total value of the bills is $100. We can represent this using the equation:
5x + 10y = 100
Now, we have a system of two equations that we can solve simultaneously to find the values of x and y.
One way to solve this system of equations is by substitution.
From the first equation, we can solve for x in terms of y:
x = 12 - y
Substituting this expression for x into the second equation, we get:
5(12 - y) + 10y = 100
Distributing the 5, we have:
60 - 5y + 10y = 100
Combining like terms:
5y = 40
Dividing both sides by 5, we get:
y = 8
Now, substitute this value of y back into the first equation to find x:
x + 8 = 12
x = 4
Therefore, Anna has 4 $5 bills and 8 $10 bills.
To check if these values are correct, we can substitute them into the original equations:
4 + 8 = 12 (correct)
5(4) + 10(8) = 100 (correct)
So, your final answer is x = 4, y = 8.
In summary, your approach was correct, but there was an error in your calculations. By solving the system of equations correctly, you determined that Anna has 4 $5 bills and 8 $10 bills.