Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.
Let the cost of one guitar pick be c.
The cost of one guitar string is c + $1.
The total cost of the guitar picks is 25c.
The total cost of the guitar strings is 25(c + $1).
The total cost of the supplies is 25c + 25(c + $1) = $40.
Combining like terms, we get 25c + 25c + $25 = $40.
Combining like terms again, we get 50c + $25 = $40.
Subtracting $25 from both sides, we get 50c = $15.
Dividing both sides by 50, we get c = $0.30.
The cost of one guitar string is $0.30 + $1 = $\boxed{1.30}.
To find the cost of one guitar string, we first need to determine the cost of one guitar pick.
Let's assume the cost of one guitar pick is c dollars.
Given that Patrick bought 25 guitar picks, the total cost of the guitar picks would be 25c dollars.
We also know that the cost of 25 guitar strings is $1 more than the cost of the guitar picks. This means that the cost of the 25 guitar strings would be (25c + $1) dollars.
According to the information given, Patrick spent a total of $40, so we can set up the following equation:
25c + $1 = $40
To solve for c, we will isolate it on one side of the equation by subtracting $1 from both sides:
25c = $40 - $1
25c = $39
Now, we can solve for c by dividing both sides of the equation by 25:
c = $39 / 25
c = $1.56
Therefore, the cost of one guitar pick is $1.56.
To find the cost of one guitar string, we can substitute the value we found for c into the formula (25c + $1):
Cost of one guitar string = (25 * $1.56) + $1 = $39 + $1 = $40
Thus, the cost of one guitar string is $40.
Let's solve this step-by-step.
Step 1: Let's assume the cost of one guitar pick is "c" dollars.
Hence, the cost of 25 guitar picks would be 25c dollars.
Step 2: We are given that the cost of 25 guitar strings is $1 more than the cost of 25 guitar picks.
So, the cost of 25 guitar strings would be (25c + $1) dollars.
Step 3: We are also given that Patrick spent a total of $40.
Therefore, the equation for his total spending can be written as:
25c + (25c + $1) = $40
Step 4: Simplify the equation.
Combining like terms, we get:
50c + $1 = $40
Step 5: Solve for c.
Subtract $1 from both sides of the equation:
50c = $40 - $1
50c = $39
Step 6: Divide both sides of the equation by 50 to isolate c.
c = $39 / 50
Step 7: Simplify the division.
c ≈ $0.78
Therefore, the cost of one guitar pick is approximately $0.78.
Step 8: We need to find the cost of one guitar string, which is $1 more than the cost of a guitar pick.
The cost of one guitar string would be:
$0.78 + $1 = $1.78
Therefore, the cost of one guitar string is $1.78.
Find x 1/4 (x+3) = 5
To find the value of x, we can solve the equation step-by-step.
Step 1: Distribute the 1/4 to the terms inside the parentheses:
1/4 (x+3) = 5
(1/4) * x + (1/4) * 3 = 5
x/4 + 3/4 = 5
Step 2: Combine like terms on the left side of the equation:
x/4 + 3/4 = 5
(x + 3)/4 = 5
Step 3: Multiply both sides of the equation by 4 to eliminate the fraction:
4 * (x + 3)/4 = 5 * 4
(x + 3) = 20
Step 4: Subtract 3 from both sides of the equation:
(x + 3) - 3 = 20 - 3
x = 17
Therefore, the value of x is 17.