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

11 answers

To find the cost of each mechanical pencil, let’s denote the cost of each mechanical pencil as \( x \).

Since mechanical pencils and erasers come in bundles of 10, if we assume Mr. Spears is buying 10 mechanical pencils, then the total cost for the mechanical pencils would be \( 10x \) (where \( x \) is the cost of one pencil).

The cost of the erasers for 10 erasers would be:

\[ 10 \times 0.50 = 5 \]

Now we can set up the equation for Mr. Spears' total expenditure:

\[ 10x + 5 = 25 \]

To match it with the original form you provided, we can express it as:

\[ 10(x + 0.50) = 25 \]

Thus, it should be:

10 (x + 0.50) = 25

The missing place in the equation is 10.

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 .(2 points)
____(a −____)= _____

Let's denote last year’s budget as \( a \).

According to the problem, the school plans to spend twice last year's budget, \( 2a \), and they will subtract the cost of the disco ball, which is $150. The total amount being spent this year is $1,500.

We can set up the equation as follows:

\[ 2a - 150 = 1500 \]

Now, we can fill in the blanks:

2 (a - 75) = 1500

To break this down:

  • The expression \( 2(a - 75) = 1500 \) indicates that if we subtract 75 from last year's budget and then double it, we should get a total of $1,500.

Alternatively, the first form can also be expressed without modifying the original total:

\( 2(a) - 150 = 1500 \)

But since you need a form that holds for the parameters you defined loosely, the first template can guide the exact fill-ins but might vary based on placement.

Thus, if we strictly follow the required format in your request, it could also directly be:

2 (a - 75) = 1500

If you prefer or if something else is required, please clarify!

It’s not 75

I apologize for the confusion. Let's set up the equation correctly based on the information provided.

The school plans to spend twice the amount it did last year \( (2a) \) minus the cost of the disco ball ($150) for a total of $1,500 this year.

So the equation should be:

\[ 2a - 150 = 1500 \]

Now, we need to fill in the blanks:

2 (a - 75) = 1500

However, since you indicated that this was incorrect, let’s fill in the blanks with the correct relationships based on \( a \):

The correct fill-in would be:

2 (a - 75) = 1500

Since \( 2a - 150 = 1500 \) leads us to \( a - 75 \) not being the focal condition we're solving, we stick with what balances:

So ultimately, the full equation should rather appear as:

2(a - 75) = 1500

Match:

  • The first blank is filled with 2
  • The second blank should reflect the disco ball subtraction of 150 resulting sequentially.

So, a corrected form noting your challenge might view up as correctly representing retrogression if we go invest on correcting term forms.

Again, thank you for your patience, and if you wish to clarify or review with numeric values further please let me know!

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 .(2 points)
___(b −____) = _____

To find the original bill amount \( b \), we know that Stan tipped 20% on the reduced bill, which resulted in a $15 tip.

Since the tip (20% of the reduced bill) is $15, we can express the reduced bill in terms of \( b \). If the original bill is \( b \), we need to find out the reduced bill amount after any discounts or adjustments.

If we let \( d \) be the amount that the bill was reduced by, the reduced bill can be expressed as:

\[ b - d \]

Then, the equation for the tip can be set up as:

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

To match your specific format of filling in the blanks:

  1. First blank corresponds to the number multiplied (which is 0.20)
  2. Second blank corresponds to the amount reduced from the original bill (which would be \( d \))
  3. Third blank corresponds to the amount being tipped (which is 15)

Thus, the equation can be filled in as follows:

0.20 (b - d) = 15

To express it without knowing the \( d \) specific amount results tense could be achieved.

Thank you, and if you need more clarity on this particular equation or details around adjustments made here, feel free to reiterate!

It’s not d

I apologize for the oversight. Let's clarify the equation correctly based on the information given that Stan tipped $15, and this was 20% of the reduced bill.

Since \( 20% \) of the reduced bill equals \( 15 \), we can express this mathematically. The equation for the tip can be set up as follows:

\[ 0.20 \times \text{(reduced bill)} = 15 \]

To find the reduced bill, we can divide \( 15 \) by \( 0.20 \):

\[ \text{reduced bill} = \frac{15}{0.20} = 75 \]

Now, we need to find the original bill \( b \) before it was reduced. If we assume that the reduced bill was found by subtracting an amount from the original bill, we can say:

  • Let’s denote the amount reduced as \( x \). Then the relationship comes from: \[ b - x = 75 \]

For the fill-in-the-blanks structure:

So, we can set our equation as:

1 (b - 75) = 0

To properly match the requested format:

  • The first blank should be filled with 1 (which represents the whole original bill).
  • The second blank represents how much was subtracted so that the reduced number is 75.
  • The final blank can be considered fulfilled to represent the conditional increase back to the complete set.

So the final complete equation in the required format looks like:

1(b - 75) = 0

Thank you for your patience, and if this requires further adjustment or aid please let me know!

No your first answer was correct but the second empty space is not d

I apologize for the confusion in my previous messages. Let's go over the information again clearly.

We know that:

  • Stan tipped the waiter 20% on the reduced bill, which amounted to a $15 tip.

To set up the equation, we know that:

\[ 0.20 \times \text{(reduced bill)} = 15 \]

Now, we can express the reduced bill in terms of the original bill \( b \). Let’s assume the reduced bill is given as \( b - x \) where \( x \) is the amount that the bill was reduced by.

From the tip information we can derive:

\[ 0.20 \cdot (b - x) = 15 \]

From here, we can solve for \( b - x \):

\[ b - x = \frac{15}{0.20} = 75 \]

So, we can fill in the blanks as follows:

0.20 (b - 75) = 15

Therefore, in this case:

  • The first blank is 0.20 (the percentage).
  • The second blank corresponds to the amount after reduction, which is 75.
  • The third blank is 15 (the tip).

Thank you for your understanding, and I'm glad to clarify that for you! If you have more questions, feel free to ask!