A school plans to spend twice the amount it did last year on its winter dance, less the cost of the disco ball which was $150, since they have it from last year. A total of $1,500 is being spent this year. Fill in the blanks to write an equation that will determine the amount of last year’s budget, a .

Question

__(a-__)=___

Answer 1

To determine last year's budget (let's call it \( a \)), we know that the school is spending twice last year's budget minus the cost of the disco ball this year.

The total amount spent this year is $1,500, and the cost of the disco ball is $150.

The equation can be set up as follows:

\[ 2a - 150 = 1500 \]

Now, to make it fit the fill in the blanks format:

Fill in the blanks:

(a - 150) = 1500 (Here \( a \) should be multiplied by 2 before subtracting 150.)

So, to rearrange slightly to fit exactly as per your requirement:

(2a - 150) = 1500

So, \[ a - 150 = 1500 \] is not completely correct as it should be: \[ 2a - 150 = 1500 \]

Final answer to fill in: (a - 150) = 1500 (Again, \( a \) would not equal 1500 in a strict sense because of the multiplication by 2. You might want to keep the equation \( 2a - 150 = 1500 \) for a correct representation.)

Thus, the clearer representation would be \( (2a - 150) \) equaling 1500 from last year's spending.

For your format strictly based on the blank filling request, the accurate dimension would be: \( (2a) - 150 = 1500 \) (expanding the right characterization accordingly).

Answer 2

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-__)=___

Answer 3

To determine the original bill \( b \), we need to account for the $12 dessert that was removed from the original bill and the 20% tip that Stan left based on the reduced bill.

1. The original bill is \( b \).
2. After removing the $12 dessert, the reduced bill becomes \( b - 12 \).
3. Stan tipped the waiter 20% on the reduced bill, which can be expressed as \( 0.20 \times (b - 12) \).
4. According to the problem, the tip amount is $15.

Putting this information together, we can write the equation:

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

Now, to rewrite this in the fill-in-the-blank format you requested:

Fill in the blanks:

(b - 12) = 15

So, the final equation based on your request is:

(b - 12) = 15 where \( 0.20 \) would be factored into the original.

To rearrange this properly in terms of straightforwardness, the precise fill would involve bringing the 0.20 out as shown in detail but focusing just on \( b - 12 \).

Please ensure the equation accurately reflects how Stan's bill and the process of calculating the tip relate to one another.

Answer 4

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.
Each puzzle cost $__

Answer 5

Let the original cost of each puzzle be \( x \).

Molly bought 6 jigsaw puzzles, and each puzzle is discounted by $0.50. Therefore, the cost after the discount for each puzzle is \( x - 0.50 \).

The total amount spent by Molly on the puzzles can be expressed as:

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

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

1. Distribute the 6:

\[ 6x - 3 = 27 \]

2. Add 3 to both sides:

\[ 6x = 27 + 3 \] \[ 6x = 30 \]

3. Divide by 6:

\[ x = \frac{30}{6} \] \[ x = 5 \]

Thus, the original cost of each puzzle was $5.

So the answer is:

Each puzzle cost $5.

Answer 6

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.
Each person ate __ mozzarella sticks.

Answer 7

Let’s break down the information provided to find out how many mozzarella sticks each person ate:

1. Total number of people: Ethan and his 7 friends make a total of \( 8 \) people.
2. Total pieces of food: There are \( 64 \) pieces of food.
3. Pizza slices per person: Each person had \( 5 \) slices of pizza.

Now, we'll first calculate the total number of pizza slices consumed by everyone:

\[ \text{Total slices of pizza} = 8 \text{ people} \times 5 \text{ slices/person} = 40 \text{ slices of pizza} \]

Next, we know the total number of pieces of food is \( 64 \), which includes both pizza slices and mozzarella sticks. Therefore, we can find the number of mozzarella sticks:

\[ \text{Total pieces of food} = \text{Pizza slices} + \text{Mozzarella sticks} \] \[ 64 = 40 + \text{Mozzarella sticks} \] \[ \text{Mozzarella sticks} = 64 - 40 = 24 \]

Now, since there are \( 8 \) people, we can find out how many mozzarella sticks each person ate:

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

Thus, each person ate 3 mozzarella sticks.

So the answer is:

Each person ate 3 mozzarella sticks.

Answer 8

solve for x:
5x-7=3
x=__

Answer 9

To solve the equation \( 5x - 7 = 3 \), follow these steps:

1. Add 7 to both sides of the equation to isolate the term with \( x \):

   \[ 5x - 7 + 7 = 3 + 7 \]

   This simplifies to:

   \[ 5x = 10 \]

2. Divide both sides by 5 to solve for \( x \):

   \[ x = \frac{10}{5} \]

   This simplifies to:

   \[ x = 2 \]

So the final answer is:

\( x = 2 \)