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 does Anna have? is this how i do this?
x+y=12
5x+10y=100
y=12-x
5x+10(12-x)
5x+120-10x=100
5x-10x=2-5x=20
x4
y8
Looks good to me.
Matt
Yes, you have correctly solved the problem using a system of equations. Let's go through the steps to get to the solution:
1. Let's define the variables:
- Let x represent the number of $5 bills.
- Let y represent the number of $10 bills.
2. Use the given information to set up the equations:
- We know that Anna has a total of 12 bills, so the first equation is: x + y = 12.
- The total value of the bills is $100, so the second equation is: 5x + 10y = 100.
3. Now, let's solve the system of equations. You used the substitution method, which is absolutely correct:
- Firstly, use x + y = 12 to express y in terms of x. Rearrange the equation to get y = 12 - x.
- Substitute this expression for y in the second equation: 5x + 10(12 - x) = 100.
- Simplify the equation by distributing: 5x + 120 - 10x = 100.
- Combine like terms: -5x + 120 = 100.
- Subtract 120 from both sides: -5x = -20.
- Divide both sides by -5: x = 4.
4. Now that you have the value of x, substitute it back into the first equation to find y: x + y = 12.
- Substitute x = 4 into the equation: 4 + y = 12.
- Subtract 4 from both sides: y = 8.
So, the solution is x = 4 and y = 8. Anna has 4 $5 bills and 8 $10 bills in her wallet.