Question

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= _____

Answer 1

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

Answer 2

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

Answer 3

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. \(x = 17\).

Answer 4

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**.

Answer 5

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**.