Question 1

Question

A)Mr. Spears was purchasing supplies for his math classroom. He had $25 to spend. Mechanical pencils and erasers come in bundles of 10. Each eraser costs $0.50. Fill in the missing place in the equation to compute the cost of each mechanical pencil.(1 point)
$$(x + 0.50)=25
(
𝑥

+

0.50
)
=
25
Question 2
A)Stan took Lily to his friend’s restaurant on a date. The friend told the waiter to remove the $12 dessert from Stan’s bill. Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. Fill in the blanks to write an equation that will determine the amount of the original bill, b
𝑏
.(2 points)
$$(b −
𝑏

−
$$) =
=
$$

Answer 1

Question 1:

To compute the cost of each mechanical pencil, we need to represent the cost of one mechanical pencil as \( x \). Since erasers cost $0.50 and Mr. Spears has a total of $25, we can write the equation as follows:

\[ x + 0.50 = 25 \]

The missing place in the original equation is the total cost of the mechanical pencil, which is represented by \( x \).

---

Question 2:

Stan tipped the waiter 20% on the reduced bill after the $12 dessert was removed. Based on the information given, the equation to determine the amount of the original bill \( b \) can be written as follows:

After removing the dessert, the reduced bill becomes \( b - 12 \). Since he tipped 20% on this reduced bill and the tip was $15, we can express this as:

\[ 0.20(b - 12) = 15 \]

So the filled-in equation will look like this:

\[ (b - 12) = \frac{15}{0.20} \]

You can also express it as:

\[ 15 = 0.20(b - 12) \]

Answer 2

So just give me the answers of the questions.

Answer 3

Sure! Here are the direct answers:

Question 1: \( x + 0.50 = 25 \) (where \( x \) is the cost of each mechanical pencil)

Question 2: \( (b - 12) = 15 / 0.20 \) (to find \( b \), the original bill)

Or simply, \( 0.20(b - 12) = 15 \).

Answer 4

Question 3
A)Molly has 6 grandchildren. She likes to be fair and buy gifts for all of them at the same time. She found jigsaw puzzles, each discounted by 50¢. Find the original cost of each puzzle if she spent a total of $27.(1 point)
Each puzzle cost $$$.
Question 4
A)Ethan had 7 of his friends over. He ordered cheese pizzas and mozzarella sticks for the 8 of them. In all, there were 64 pieces of food. If each person had 5 slices of pizza, find the number of mozzarella sticks each person ate.(1 point)
Each person ate $$ mozzarella sticks.
Question 5
A)Jason’s age is 1/2
1
2
the difference of his mother’s age and 6. Jason is 16. How old is Jason’s mother?(1 point)
$$ years old

Answer 5

Here are the answers to your questions:

Question 3: Let \( x \) be the original cost of each puzzle. Since Molly spent a total of $27 for 6 puzzles, we can set up the equation:

\[ 6(x - 0.50) = 27 \]

Solving for \( x \):

\[ 6x - 3 = 27 \] \[ 6x = 30 \] \[ x = 5 \]

Each puzzle cost $5.00.

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Question 4: Each person had 5 slices of pizza, and there were 8 people in total. Thus, the total number of pizza slices consumed is:

\[ 8 \times 5 = 40 \text{ slices} \]

Given that there were a total of 64 pieces of food, we can find the number of mozzarella sticks:

\[ 64 - 40 = 24 \text{ mozzarella sticks} \]

To find the number of mozzarella sticks each person ate:

\[ \frac{24 \text{ sticks}}{8 \text{ people}} = 3 \text{ sticks per person} \]

Each person ate 3 mozzarella sticks.

---

Question 5: Let \( m \) be Jason's mother's age. The equation given based on the statement is:

\[ 16 = \frac{1}{2}(m - 6) \]

Multiplying both sides by 2 to eliminate the fraction:

\[ 32 = m - 6 \] \[ m = 38 \]

Jason's mother is 38 years old.

Answer 6

Stan took Lily to his friend’s restaurant on a date. The friend told the waiter to remove the $12 dessert from Stan’s bill. Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. Fill in the blanks to write an equation that will determine the amount of the original bill, b
𝑏
.(2 points)
(b −
𝑏

−
12) =
=

Answer 7

To determine the amount of the original bill \( b \), we can set up the equation based on the information given.

1. The reduced bill after removing the $12 dessert is \( b - 12 \).
2. Stan tipped 20% on the reduced bill, and the tip was $15.

The equation can be represented as:

\[ 0.20(b - 12) = 15 \]

If we want to fill in the blanks based on your question, we can express it in the specific form you provided:

\[ (b - 12) = \frac{15}{0.20} \]

So, the completed statement with the blanks filled in would be:

Fill in the blanks:
\( (b - 12) = \frac{15}{0.20} \)

This can also be simplified further:

\[ (b - 12) = 75 \]

Thus the final equation can also be stated as:

\[ b - 12 = 75 \]

So \( b = 75 + 12 = 87 \), meaning the original bill \( b \) would be $87.

Answer 8

Wrong

Answer 9

I apologize for the confusion. Let's go through the equation again step by step.

1. Identify the Reduced Bill:

   • The original bill is \( b \).
   • After removing the $12 dessert, the reduced bill is \( b - 12 \).

2. Calculate the Tip:

   • Stan tipped 20% on the reduced bill, which amounted to $15.
   • The equation for the tip can be written as: \[ 0.20(b - 12) = 15 \]

So, to fill in the blanks for the equation that determines the original bill \( b \):

Equation:
\[ (b - 12) = \frac{15}{0.20} \]

To calculate \( \frac{15}{0.20} \): \[ \frac{15}{0.20} = 15 \div 0.20 = 75 \]

Thus, the equation can also be stated as: \[ (b - 12) = 75 \]

From here, to solve for \( b \): \[ b - 12 = 75 \implies b = 75 + 12 \implies b = 87 \]

Final Result:

1. The equation is \( (b - 12) = 75 \).
2. The original bill \( b \) is $87.

Thank you for your patience, and I hope this clarifies everything!