Answer:
5n + 100n = 210
Peggy has 8 quarters and 2 nickels
Step-by-step explanation:
Let's call q the number of quarters and n the number of nickels.
If Peggy has four times as many quarters as nickels, we can write the following equation:
q = 4n
Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so
0.25q + 0.05n = 2.10
Because she had $2.10. Now, we can replace the first equation on the second one
0.25(4n) + 0.05n = 2.10
1n + 0.05n = 2.10
Finally, we can multiply both sides by 100, so
100n + 0.05(100)n + 2.10(100)
100n + 5n = 210
Therefore, the equation that can be used to solve the problem is
5n + 100n = 210
Now, we can solve the equation for n
105n = 210
105n/105 = 210/105
n = 2
Then, q is equal to
q = 4n
q = 4(2)
q = 8
It means that Peggy has 8 quarters and 2 nickels.