Damari is selling popcorn for $3 a bag. He already has $40, and his goal is to earn $85 total. Use arithmetic to determine how many bags he needs to sell to make his goal?

Answer 1

To find out how many bags of popcorn Damari needs to sell to reach his goal of $85, we can set up the equation using the information given.

Damari currently has $40 and wants to make a total of $85.

First, we find out how much more money he needs to earn:

\[ 85 - 40 = 45 \]

Next, we know that each bag of popcorn sells for $3. We can find the number of bags \( x \) he needs to sell by dividing the additional amount he needs by the price per bag:

\[ x = \frac{45}{3} = 15 \]

Therefore, Damari needs to sell 15 bags of popcorn to reach his goal of $85.

Answer 2

Damari is selling popcorn for $3 a bag. He already has $40, and his goal is to earn $85 total. Use arithmetic to determine how many bags he needs to sell to make his goal

Answer 3

To find out how many bags of popcorn Damari needs to sell, we can break it down as follows:

1. Calculate the amount of money Damari still needs to reach his goal: \[ \text{Goal} - \text{Current Amount} = \text{Amount Needed} \] \[ 85 - 40 = 45 \]

2. Determine how many bags of popcorn he needs to sell to earn that amount: Each bag of popcorn sells for $3, so we divide the amount needed by the price of one bag: \[ \text{Bags Needed} = \frac{\text{Amount Needed}}{\text{Price per Bag}} = \frac{45}{3} = 15 \]

Therefore, Damari needs to sell 15 bags of popcorn to reach his goal of $85.

Answer 4

Nya is building a garden in her yard. She has 24 feet of fencing for her garden and wants it to be in the shape of a rectangle with a length of 3 feet. What does the width need to be for this to work?

Answer 5

To find the width that Nya needs for her rectangular garden, we can use the formula for the perimeter of a rectangle:

\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]

Nya has 24 feet of fencing, so we can set up the equation as follows:

\[ 24 = 2 \times (3 + \text{Width}) \]

Now, let's solve for the width:

1. Divide both sides by 2: \[ 12 = 3 + \text{Width} \]

2. Subtract 3 from both sides: \[ \text{Width} = 12 - 3 \] \[ \text{Width} = 9 \]

Therefore, the width of Nya's garden needs to be 9 feet.

Answer 6

Stacia wanted concert tickets that were selling for $36 each, and then she got a $19 discount. She paid a total of $53 for the tickets. How many tickets did she buy? Identify the operations needed to solve this problem using the equation  36x −19=53

Answer 7

To determine how many concert tickets Stacia bought, we can start with the equation provided:

\[ 36x - 19 = 53 \]

In this equation:

• \( x \) represents the number of tickets Stacia purchased.
• $36 is the price per ticket.
• $19 is the discount she received.
• $53 is the total amount she paid after the discount.

Steps to Solve the Equation

1. Add 19 to both sides: This step will eliminate the discount from the left side. \[ 36x - 19 + 19 = 53 + 19 \] \[ 36x = 72 \]

2. Divide both sides by 36: This will isolate \( x \) to find the number of tickets. \[ x = \frac{72}{36} \] \[ x = 2 \]

Conclusion

Stacia bought 2 tickets.

Operations Identified

To summarize the operations needed to solve this problem:

1. Addition (to eliminate the discount): \( +19 \)
2. Division (to find the number of tickets): \( \div 36 \)

These operations lead to the conclusion that Stacia purchased 2 tickets.

Answer 8

Niel has a bucket of beads. He uses them to make 8 identical necklaces and then buys 25 beads at the store. He ends up with a total of 500 beads. How many did he start with? Identify the operations needed to solve this problem using the equation  b/8 + 25 = 500

Answer 9

To find out how many beads Niel started with, we first analyze the equation given:

\[ \frac{b}{8} + 25 = 500 \]

In this equation:

• \( b \) represents the number of beads Niel initially had.
• \( \frac{b}{8} \) signifies the number of beads used for making 8 identical necklaces.
• 25 is the number of beads Niel bought at the store.
• 500 is the total number of beads he ended up with.

Steps to Solve the Equation

1. Subtract 25 from both sides: This eliminates the 25 beads he bought. \[ \frac{b}{8} + 25 - 25 = 500 - 25 \] \[ \frac{b}{8} = 475 \]

2. Multiply both sides by 8: This isolates \( b \) to find the total number of beads he started with. \[ b = 475 \times 8 \] \[ b = 3800 \]

Conclusion

Niel started with 3800 beads.

Operations Identified

To summarize the operations needed to solve this problem:

1. Subtraction (to remove the number of beads bought): \( -25 \)
2. Multiplication (to find the initial number of beads): \( \times 8 \)

These operations lead to the conclusion that Niel initially started with 3800 beads.

Answer 10

A window cleaner has enough supplies to clean 21 windows per office building on a certain number of buildings. They can also clean the windows of a school with 42 windows. Altogether, there are enough supplies to clean 126 windows. How many office buildings can be washed? Identify the equation that would be used to solve this problem algebraically

Answer 11

To determine how many office buildings can be washed, we can set up an equation based on the information given.

Let \( x \) be the number of office buildings cleaned. Each office building has enough supplies to clean 21 windows, and there is also one school with 42 windows. The total number of windows that can be cleaned is 126.

Setting Up the Equation

Given that:

• Windows cleaned per office building = 21
• Windows cleaned for the school = 42
• Total windows cleaned = 126

We can represent the total number of windows cleaned with the following equation:

\[ 21x + 42 = 126 \]

Where:

• \( 21x \) represents the total number of windows from \( x \) office buildings.
• \( 42 \) represents the windows of the school.
• The sum equals the total number of windows, which is 126.

Solving for \( x \)

1. Subtract 42 from both sides: \[ 21x + 42 - 42 = 126 - 42 \] \[ 21x = 84 \]

2. Divide by 21: \[ x = \frac{84}{21} \] \[ x = 4 \]

Conclusion

So, the number of office buildings that can be cleaned is 4.

Summary of the Equation

The equation that can be used to solve this problem is:

\[ 21x + 42 = 126 \]

This equation represents the relationship between the number of office buildings and the total number of windows cleaned.