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 x be the cost of one guitar string.

The cost of one guitar pick is x - 1 because they only cost $1 more than the guitar picks.
The total amount Patrick spent on guitar picks is 25 * (x - 1) = 25x - 25.
The total amount he spent on guitar strings is 25 * x.
The combined total cost is 25x - 25 + 25x = 50x - 25.
50x - 25 = 40.
50x = 40 + 25.
50x = 65.
x = 65 / 50.
x = <<65/50=1.30>>1.30. Answer: \boxed{1.30}.

Fill in the spaces to solve each step of the problem 1/4(x+3)=5.(2 points)

Step 1: ( )1/4(x+3)=5( ).
Step 2: x+3=
Step 3: Subtract from both sides.
Step 4: x=

Step 1: ( )1/4(x+3)=5( )

Step 2: x+3= <<1/4(x+3)=5*x/1=5*x=5*4=20>>20

Step 3: Subtract from both sides.

Step 4: x= 20-3= <<20-3=17>>17

No, you are suppose to fill in the blanks.

I apologize for the confusion. Here is the updated response:

Step 1: (Multiply both sides by 4)
1/4(x+3)=5
Step 2: x+3= ___
Step 3: Subtract 3 from both sides:
x = ___

Thank you.

You're welcome! If you have any more questions, feel free to ask.

Marbles come in two sizes: 1-inch diameter and 2-inch diameter. The 1-inch diameter marbles cost 30 cents less than the 2-inch marbles. Rochelle buys 25 1-inch marbles for her science project and spends exactly $10. Find the cost of a 2-inch marble.(1 point)

Responses

$2.80
$2.80

$0.10
$0.10

$2.50
$2.50

$0.70

Let's assume the cost of a 2-inch diameter marble is x cents.

According to the given information, the cost of a 1-inch diameter marble is x - 30 cents.
Rochelle buys 25 1-inch marbles for a total cost of $10, which is equal to 1000 cents.
So, the equation representing this situation is:
25(x - 30) = 1000
Simplifying the equation:
25x - 750 = 1000
Adding 750 to both sides of the equation:
25x = 1750
Dividing both sides of the equation by 25:
x = 70
Therefore, the cost of a 2-inch marble is $0.70.
The correct option is $0.70

A local dumpling shop sold 85,248 dumplings last year. Each plate of dumplings sells for $9.89, and there are 12 dumplings per plate. Which value best estimates the shop’s total earnings from selling dumplings?(1 point)

Responses

8,000,000
8,000,000

800,000
800,000

80,000
80,000

8,000

To find the shop's total earnings from selling dumplings, we need to multiply the number of plates sold by the price per plate.

The number of plates sold is given by dividing the total number of dumplings sold by the number of dumplings per plate:
Number of plates sold = 85,248 dumplings / 12 dumplings per plate = 7104 plates.

The total earnings from selling dumplings is then calculated by multiplying the number of plates sold by the price per plate:
Total earnings = 7104 plates * $9.89 per plate = $70,375.56.

Therefore, the value that best estimates the shop's total earnings from selling dumplings is $70,375.56.