Final answer:
To determine the number of dimes and quarters Devont had, we can set up a system of linear equations based on the given information. The first equation is D + Q = 41 and the second equation is 0.10D + 0.25Q = 7.55. By solving this system using substitution, we find that Devont had 18 dimes and 23 quarters.
Step-by-step explanation:
To determine the number of dimes and quarters Devont had, we can set up a system of linear equations based on the given information. Let's say the number of dimes is represented by D and the number of quarters is represented by Q.
The first equation is: D + Q = 41 (since there are a total of 41 coins).
The second equation is: 0.10D + 0.25Q = 7.55 (since the value of dimes is $0.10 and the value of quarters is $0.25 and the total value of the coins is $7.55).
We can solve this system of equations either using substitution or elimination. Let's use substitution:
From the first equation, we can express D in terms of Q as D = 41 - Q. Substituting this into the second equation:
0.10(41 - Q) + 0.25Q = 7.55
4.10 - 0.10Q + 0.25Q = 7.55
0.15Q = 3.45
Q = 3.45 / 0.15
Q = 23
Substituting the value of Q back into the first equation: D + 23 = 41
D = 41 - 23
D = 18
Therefore, Devont had 18 dimes and 23 quarters.