Question

11. Jonathan has $7.00 in nickels, dimes, and quarters. He has twice as many dimes as nickels, and 3 times as many quarters as nickels. He has 42 coins altogether. How. many of each coin does he have ​

Answer 1

Jonathan has 7 nickels, 14 dimes, and 21 quarters. Solving the problem involves setting up equations based on the given information and simplifying them to find the number of each type of coin.

Step-by-step explanation:

Jonathan has $7.00 in nickels, dimes, and quarters. To solve this problem, we need to translate this into equations based on the information given:

• Let N = the number of nickels
• Let D = the number of dimes, which is twice the number of nickels (D = 2N)
• Let Q = the number of quarters, which is three times the number of nickels (Q = 3N)
• The total number of coins is 42, so N + D + Q = 42.
• The total value of the coins in cents is 700 (since $7.00 equals 700 cents), so 5N + 10D + 25Q = 700.

Substituting D and Q from the first two bullet points into the last two, we get:

• N + 2N + 3N = 42
• 5N + 10(2N) + 25(3N) = 700

Now we simplify:

• 6N = 42
• N = 7 (number of nickels)
• D = 2N = 14 (number of dimes)
• Q = 3N = 21 (number of quarters)

Therefore, Jonathan has 7 nickels, 14 dimes, and 21 quarters.

Answer 2

$7.00

Step by step Step-by-step explanation:

Let's start by using variables to represent the number of each coin.

Let x = number of nickels

Then, since Jonathan has twice as many dimes as nickels, we know:

2x = number of dimes

And since he has three times as many quarters as nickels:

3x = number of quarters

We also know that he has a total of 42 coins:

x + 2x + 3x = 42

6x = 42

x = 7

Now we can plug x back into the expressions for the number of each coin:

- Number of nickels: x = 7

- Number of dimes: 2x = 14

- Number of quarters: 3x = 21

So Jonathan has 7 nickels, 14 dimes, and 21 quarters.

To check, we can add up the value of each coin:

- Value of nickels = $0.35 (7 x $0.05)

- Value of dimes = $1.40 (14 x $0.10)

- Value of quarters = $5.25 (21 x $0.25)

Total value = $7.00

So our answer is correct.