Question

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?

Answer 1

Answer:

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.

Answer 2

The fewest number of dimes Danielle could have in his piggy bank is 4

Recall :

1 nickel = 5 cent = $0.05

1 dime = 10 cent = $0.1

Let;

number of nickel = n

Number of dime = d

Total number of coins = 25

n + d = 25 - - - (1)

0.05n + 0.1d ≥ 1.44 - - - (2)

From (1)

n = 25 - d

Put n = 25 - d in (2)

0.05(25 - d) + 0.1d  ≥ 1.44

1.25 - 0.05d + 0.1d  ≥ 1.44

1.25 + 0.05d ≥ 1.44

0.05d ≥ 1.44 - 1.25

0.05d ≥ 0.19

d  ≥0.19 / 0.05

d ≥ 3.8

The least whole number value which satisfies the inequality is 4 ;

Hence, d = 4

Hence, fewest number of dimes is 4

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