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= _____

5 answers

Let's solve the equation \( \frac{1}{4}(x+3) = 5 \) step by step and fill in the spaces accordingly.

Step 1: (4) \(\frac{1}{4}(x+3) = 5(4)\). Step 2: \(x+3 = 20\). Step 3: Subtract \(3\) from both sides. Step 4: \(x = 17\).

So, your filled-in steps are:

  1. (4) \(\frac{1}{4}(x+3) = 5(4)\).
  2. \(x+3 = 20\).
  3. Subtract \(3\) from both sides.
  4. \(x = 17\).
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

$0.70
$0.70

$2.50
$2.50

$0.10
$0.10

$2.80

Let the cost of a 2-inch marble be \( x \) dollars. Since the 1-inch marbles cost 30 cents less, the cost of a 1-inch marble will be \( x - 0.30 \) dollars.

Rochelle buys 25 1-inch marbles for a total of $10. Therefore, we can write the equation:

\[ 25(x - 0.30) = 10 \]

Now, let's solve for \( x \):

  1. Distribute the 25: \[ 25x - 7.50 = 10 \]

  2. Add 7.50 to both sides: \[ 25x = 17.50 \]

  3. Divide by 25: \[ x = \frac{17.50}{25} = 0.70 \]

So, the cost of a 2-inch marble is $0.70.

The correct response 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

800,000
800,000

8,000
8,000

8,000,000
8,000,000

80,000

To estimate the total earnings from selling the dumplings, we first need to calculate how many plates of dumplings the shop sold:

  1. Calculate the number of plates sold: \[ \text{Number of plates} = \frac{\text{Total dumplings}}{\text{Dumplings per plate}} = \frac{85,248}{12} \] Dividing gives: \[ \text{Number of plates} = 7,104 \]

  2. Calculate total earnings: \[ \text{Total earnings} = \text{Number of plates} \times \text{Price per plate} = 7,104 \times 9.89 \] To simplify this estimation, we can round \(9.89\) to approximately \(10\): \[ \text{Total earnings} \approx 7,104 \times 10 = 71,040 \]

Based on these calculations, the best estimate of the shop's total earnings would be closest to the value 80,000.

So, the correct response is:

80,000.