Question

A purse contains dimes and nickels. The total value of all the coins is, at most, $2.50, and there are at least three of each coin. Which of the following systems correctly shows the system that describes the possible number of nickels (n) and dimes (d) in the purse?

<= That means greater than or equal to or less than or equal to

1.n >= 3
d >= 3
0.05n+0.1d <= 2.50

2. n <= 3
d <= 3
0.05+0.1d <= 2.50

3. n <= 3
d<= 3
n + d >= 2.50

4. n>=3
d >= 3
n + d <=2.50

Answer 1

The answer is 3. If it says "at most", that means that the total value of money has to be less than or equal to 2.50. Same thing with "at least." There would have to be more than 3 of each coin because 3 nickels and 3 dimes don't add up to 2.50. 

Answer 2

1 is the correct answer. d and n each have to be at least three, so the sign is correct. also, the sum of nickels and dimes is at most 2.50, so the sign is correct there, too.