Help please?

Question

Suppose Tom has 24 coins totaling $3.75. If he has only dimes and quarters, how many of each type does he have?

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to put together algebraic expressions that relate the variables to one another. On this one we have

D + Q = 24   because there are 24 coins in total

10D + 25Q = 375   because dimes are worth 10 cents, quarters are worth 25 cents, and there are 375 cents = $3.75 in total

From there then you can solve for the value algebraically! I think the best way is to substitute the first equation into the second equation as Q = 24 – D and then solve for the value of Q algebraically.

When I do that I get Q = 9 and D = 24 – 9 = 15, meaning that Tom has 9 quarters and 15 dimes.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

So if he has 24 coins, you can write the equation D + Q = 24.

If their worth is 3.75, you can write .10D + .25Q = 3.75.

 

There are many methods to solve this depending on how you've been taught, but your answer is D=15, Q=9.

 

Hope you can solve this system of equations.