Question

Scott bought a pen and received change of $4.75 in 25 coins, all dimes and quarters. How many of each kind did he receive?

Answer 1

Scott received 10 dimes and 15 quarters as change. This problem is solved by setting up and solving a system of linear equations based on the number of coins and their total value.

Step-by-step explanation:

The student is asking about a problem involving coin counting and the use of linear equations to find the number of dimes and quarters that make up a total of $4.75 in 25 coins. To solve this, we use two equations based on the number of coins and their total value. Let's define the number of dimes as 'd' and the number of quarters as 'q'.

Step 1: Set up the equations

Since there are 25 coins in total, we have:

d + q = 25 (Equation 1)

Since the total amount of money is $4.75, and dimes are worth $0.10 and quarters are worth $0.25, we can write:

0.10d + 0.25q = 4.75 (Equation 2)

Step 2: Solve the system of equations

We can multiply Equation 2 by 100 to get rid of the decimals:

10d + 25q = 475

Now we can use substitution or elimination to find the values for 'd' and 'q'. Subtracting 10 times Equation 1 from this new equation gives:

10d + 25q - (10d + 10q) = 475 - 250

15q = 225

q = 225 / 15

q = 15

Substituting 'q' back into Equation 1:

d + 15 = 25

d = 25 - 15

d = 10

So, Scott received 10 dimes and 15 quarters.

Answer 2

He received 10 dimes and 15 quarters.

Step-by-step explanation:

Dimes = $0.10

Quarters = $0.25

Variable x = dimes

Variable y = quarters

Create a pair of linear equations:

0.10x + 0.25y = 4.75

x + y = 25

Isolate any variable, using an equation of your choice:

x + y = 25

x = 25 - y

Plug in this new value of x into the other equation:

0.10(25 - y) + 0.25y = 4.75

Use the distributive property:

2.5 - 0.10y + 0.25y = 4.75

Combine like terms:

2.5 + 0.15y = 4.75

Isolate variable y:

0.15y = 2.25

y = 15

Plug in the value of y into any equation:

x + y = 25

x + 15 = 25

Isolate variable x:

x = 10