Tristan has some dimes and some quarters. He has at least 20 coins worth at most $4.25 combined. If Tristan has 10 dimes, determine the maximum number of quarters that he could have. If there are no possible solutions, submit an empty answer.

The maximum number of quarters that he could have is 13

Step-by-step explanation:

Let x represent the number of quarters he could have. If he has 10 dimes and has at least 20 coins, then

→ x + 10 > = 20

→ x > = 10 (1)

His coins worth at most $4.25. Also, it is known that 1 dollar is equal to 100 cents, 1 dime is equal to 10 cents and 1 quarter is equal to 25 cents.

→ (x * 25) + (10 * 10) < = (4.25 * 100)

→ 25x + 100 < = 425

→ 25x < = 325

→ x < = 13 (2)

If we combine the equation 1 and 2:

10 < = x < = 13

The maximum value of x is 13