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Devont had a handful of dimes and quarters in his pocket. He counted 41 coins and realized they were worth $7.55. Write and solve a system of linear equations to determine the number of dimes and quarters Devont had.

User Aldux
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2 Answers

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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.

User Rohola Zandie
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6 votes

Answer:D:18 Q:23

Step-by-step explanation:

User Sayantan Mandal
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3.4k points