Question

Jai has some dimes and some quarters. He has no more than 18 coins worth at least $3.45 combined. If Jai has 4 dimes, determine all possible values for the number of quarters that he could have.

Answer 1

Jai needs at least 13 quarters to reach the $3.45 total with his 4 dimes, but cannot have more than 18 coins in total. Therefore, he can have between 13 and 14 quarters.

Step-by-step explanation:

Jai has 4 dimes and needs a combined total of at least $3.45 from his coins. Since a dime is worth $0.10 and he has 4 dimes, he already has $0.40 from the dimes. He needs at least $3.05 more to reach the $3.45 total. A quarter is worth $0.25, so we can calculate how many quarters Jai needs by dividing the remaining amount he needs by the value of a quarter:

$3.05 ÷ $0.25 = 12.2

Since Jai cannot have a fraction of a coin, he needs at least 13 quarters to reach at least $3.45. However, he cannot have more than 18 coins in total. Since he already has 4 dimes, he can have at most 14 quarters (18 coins total - 4 dimes).

Therefore, Jai can have between 13 and 14 quarters.