Question

a jar containing 67 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$7.55. How many of each type of coin do they​ have?

Answer 1

The student's question about the number of quarters and nickels in a jar is solved using a system of equations. Through this method, it is determined that the jar contains 21 quarters and 46 nickels.

Step-by-step explanation:

To solve the problem of determining how many quarters and nickels are in a jar with a total of 67 coins and a value of $7.55, we can set up a system of equations. Let's define the following variables:

• Q as the number of quarters
• N as the number of nickels

We are given two pieces of information which we can use to create our equations:

1. The total number of coins is 67: Q + N = 67
2. The total value of the coins is $7.55: 0.25Q + 0.05N = 7.55

To solve this system, we can use substitution or elimination. Let's use the elimination method:

• Multiply the second equation by 20 to get whole numbers for the coefficients: 5Q + N = 151
• Now subtract the first equation from the modified second equation: (5Q + N) - (Q + N) = 151 - 67
• This gives us 4Q = 84, and dividing by 4 gives us Q = 21. So there are 21 quarters in the jar.
• Substituting Q in the first equation: 21 + N = 67 gives us N = 67 - 21, which is N = 46.

So, the jar contains 21 quarters and 46 nickels.