Algebraic Equations for Motion and Currency: Solving for Variables

[Omid]

Here there are two question I need help with them :
1. A motor car goes m yards in t seconds. If this equals v miles per hour, write the equation connecting m, t, and v.
2. The number of cents in d dimes and n nickels is given by the equation c=10d+5n. If this equation is solved for d, the result is d=(c-5n)/10. Does this give the number of dimes in cents and n nickels ? Is the equation true if solved for n ?


I have some answers in my head for those questions but I want to know the idea behind them exactly, specially the second one. That's why I posted them.

 

[recon]

I didn't know Iran uses the American System of Units. I am not familiar with this system. Anyhow:

1. 1 mile = 1760 yards. 1 hour = 60 x 60 = 3600 seconds. So, 1 yard/sec = (1/1760)/(1/3600) miles per hour.

2. I don't quite understand the question "Does this give the number of dimes in cents and n nickels?" All I know is that d is the number of dimes you have, n is the number of nickels you have, and c the total amount of money you have (from dimes and nickels). Of course, it wouldn't be sensible to say that you have 5 1/2 dime coins when you have 55 cents because tampered coins are no good!

 

[Sirus]

1. Hint: Try to work with your units so you have only miles and hours.
2. To answer the first part of this question, try to keep in mind exactly what each variable represents in the original equation. To answer the second part, you could try to do some experimenting (substituting values) to check if the equation is true when solved for n.

 

[Omid]

I didn't know Iran uses the American System of Units

because Iran doesn't use that, the point is that I'm reading an American Algebra book.

Thanks for the answer