Robin has $6.20 in nickels and quarters. If the nickels were quarters and the quarters were nickels, he would have $3.20 more. How many quarters does Robin have?
5n+25q = 620
5q+25n = 620+320
now just solve for q.
Wall
To solve this problem, we need to set up an equation based on the given information.
Let's assume that Robin has "n" nickels and "q" quarters.
First, we can find the value of the nickels and quarters he currently has.
The value of n nickels is 5n cents.
The value of q quarters is 25q cents.
According to the given information, if the nickels were quarters and the quarters were nickels, he would have $3.20 more. This means that the value of the nickels (if they were quarters) would be 5n * 25 = 125n cents, and the value of the quarters (if they were nickels) would be 25q * 5 = 125q cents.
Given that the current total value is $6.20, we can set up the following equation:
5n + 25q = 620 (equation 1)
Based on the information that if the nickels were quarters and the quarters were nickels, he would have $3.20 more, we can set up another equation:
125n - 125q = 620 + 320 (equation 2)
Simplifying the equation, we have:
125n - 125q = 940 (equation 2 simplified)
Now, we have a system of equations (equations 1 and 2 simplified). We can solve this system to find the values of "n" and "q" which represent the number of nickels and quarters Robin has.
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the elimination method:
Multiply equation 1 by 5 to make the coefficients of "n" in both equations equal:
25n + 125q = 3100
125n - 125q = 940
Now, add the two equations together:
150n = 4040
Divide both sides by 150:
n = 26.933...
Since "n" represents the number of nickels, it cannot be a fraction. Therefore, it means that our initial assumption was incorrect. There is no exact solution to this problem.
It's possible that there was an error in the problem statement or some information is missing. Please double-check the problem, or try to provide more information to solve it accurately.