The 25 coins in danielle's piggy bank have a value of at least $1.44. the bank contains only nickels and dimes. what is the fewest number of dimes that could be in the bank?

The fewest number of dimes could be 4.

Step-by-step explanation:

Let x be the number of nickels and y be the number of dimes,

Since, total coins = 25

⇒ x + y = 25

⇒ x = 25 - y (1)

Now, 1 nickel = 0.05 dollars and 1 dimes = 0.1 dollars,

So, the total cost = 0.05x + 0.1y

According to the question,

0.05x + 0.1y ≥ 1.44

From equation (1),

0.05(25-y) + 0.1y ≥ 1.44

1.25-0.05y + 0.1y ≥ 1.44

1.25 + 0.05y ≥ 1.44

0.05y ≥ 1.44 - 1.25

0.05y ≥ 0.19

y ≥ 3.8 ≈ 4

Hence, the fewest number of dimes that could be in the bank is 4.