You have $3.20 in quarters and dimes. You gave four fewer quarters than dimes.
What is the equation for this? They also want me to then answer in augmented matrix form, but I can do that easily, I just need the equation since I just get really mixed up trying to figure it out:/ Please help? Thanks
*have... not gave
number of dimes ---- x
number of quarters --- x-4
equation based on value:
10x + 25(x-4) = 320
etc
Ok, great, thanks again Reiny!
To set up the equation for this problem, we can use the following steps:
1. Define the variables: Let's say the number of quarters is represented by 'q' and the number of dimes is represented by 'd'.
2. Translate the problem into algebraic language: We are given that the total value of the quarters and dimes is equal to $3.20. Additionally, we are told that the number of quarters is four fewer than the number of dimes.
3. Write the equation: The value of each quarter is $0.25, so the total value of the quarters is 0.25q. Similarly, the value of each dime is $0.10, so the total value of the dimes is 0.10d. Therefore, we can set up the equation as follows:
0.25q + 0.10d = 3.20 (equation 1)
Since we are also told that the number of quarters is four fewer than the number of dimes, we can write another equation expressing this relationship:
q = d - 4 (equation 2)
Now you have the system of equations that represents the given problem.
To present the system of equations in augmented matrix form, we can write it as:
[0.25 0.10 | 3.20]
[ 1 -1 | -4 ]
Alternatively, you can also rewrite the system of equations explicitly, which would be:
0.25q + 0.10d = 3.20
q - d = -4
Both forms represent the same system and can be used to find the solution.