Question

John has a total of 13 coins in his pocket. Of the 13 coins, they are all either quarters or dimes. The total value of the coins is $2.50. How many quarters does John have in his pocket?

Answer 1

John has 8 quarters in his pocket. We used algebraic equations representing the total number of coins and their total value, along with the individual values of quarters and dimes to solve the problem.

Step-by-step explanation:

The problem is to find out how many quarters John has in his pocket given that he has a total of 13 coins, which are all either quarters or dimes, and they make up a total value of $2.50. First, we should understand the value of each coin: a quarter is worth 25 cents and a dime is worth 10 cents.

Let's use algebra to solve this. If we let Q represent the number of quarters and D represent the number of dimes, we have two equations.

1. The sum of quarters and dimes equals 13: Q + D = 13
2. The total value of coins is $2.50: 0.25Q + 0.10D = 2.50

Multiplying the second equation by 100 to get rid of decimals gives us:

1. 25Q + 10D = 250

Using the first equation, we can express D in terms of Q: D = 13 - Q. Then substituting D in the second equation:

1. 25Q + 10(13 - Q) = 250

Simplifying the equation, we get:

1. 25Q + 130 - 10Q = 250
2. 15Q = 120
3. Q = 8

Therefore, John has 8 quarters in his pocket.

Answer 2

8 quarters = (8 x .25) = $2.00

5 dimes = (5 x .10) = $.50

$2.00 + $.50 = $2.50

8 + 5 = 13