Question

David and Gino each have coins with the same total value. David has a mixture of nickels and dimes and he has 8 more nickels than he has dimes. Gino only had nickels, and he has 20 more nickels than David. What is the value of David’s coins?

Answer 1

190 cents, or $1.90.

Explanation:

Let's use variables to represent the number of nickels and dimes that David has.

Let N represent the number of nickels David has.

Let D represent the number of dimes David has.

According to the information given:

1. David has 8 more nickels than dimes:

`\sf N = D + 8`

2. Gino has 20 more nickels than David:

Gino's nickels = David's nickels + 20

Gino's nickels = N + 20

Now, let's calculate the value of David's coins in terms of nickels and dimes.

The value of David's nickels (in cents) = 5 cents × N

The value of David's dimes (in cents) = 10 cents × D

The total value of David's coins is the sum of these values:

Total value = 5N + 10D

Now, let's consider Gino's coins. Gino only has nickels, so the value of his coins is given by:

Gino's total value = 5 cents × (N + 20)

Since we know that David and Gino have the same total value, we can set up an equation:

5N + 10D = 5(N + 20)

Now, let's solve this equation:

5N + 10D = 5N + 100

Subtract 5N from both sides of the equation:

10D = 100

Now, divide both sides by 10 to solve for D:

`\sf D = (100)/(10)`

D = 10

Now that we know D (the number of dimes), we can find N (the number of nickels) using the relationship N = D + 8:

N = 10 + 8

N = 18

So, David has 18 nickels and 10 dimes.

Now, let's calculate the value of David's coins:

Total value = 5N + 10D

Total value = 5(18) + 10(10)

Total value = 90 + 100

Total value = 190 cents

Therefore, the value of David's coins is 190 cents, or $1.90.