Let's solve each problem step-by-step.
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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.
First, we need to find out how much more money Damari needs to reach his goal: \[ 85 - 40 = 45 \]
He needs to earn $45 more, and since each bag of popcorn sells for $3, we can calculate the number of bags he needs to sell: \[ \frac{45}{3} = 15 \] Therefore, Damari needs to sell 15 bags.
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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?
The perimeter P of a rectangle is given by the formula: \[ P = 2 \times (length + width) \] For Nya's garden, the perimeter is 24 feet, and the length is 3 feet. Set the equation: \[ 24 = 2 \times (3 + width) \] Dividing both sides by 2: \[ 12 = 3 + width \] Subtracting 3 from both sides gives: \[ width = 12 - 3 = 9 \] Thus, the width needs to be 9 feet.
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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?
We can use the equation: \[ 36x - 19 = 53 \] First, add 19 to both sides: \[ 36x = 53 + 19 \] \[ 36x = 72 \] Next, divide both sides by 36: \[ x = \frac{72}{36} = 2 \] Therefore, Stacia bought 2 tickets. The operations needed are addition and division.
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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?
We can use the equation: \[ b + 25 = 500 \] If Niel used \( 8 \) beads per necklace, we have: \[ 8b + 25 = 500 \] To find \( b \): \[ 8b = 500 - 25 \] \[ 8b = 475 \] Dividing both sides by 8 gives: \[ b = \frac{475}{8} = 59.375 \] It appears we need a slight adjustment in interpretation. If using the whole number, let's use: \[ b = 500 - 25 = 475, \text{ (use total beads after making necklaces)}. \] However, to recheck I realize we have \( b = \frac{(500 - 25)}{8} = ... \)
The operations needed in solving \( b + 25 = 500 \) are subtraction and division.
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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.
Let \( x \) be the number of office buildings. The total number of windows can be expressed as: \[ 21x + 42 = 126 \] To isolate \( x \), we can manipulate the equation: \[ 21x = 126 - 42 \] \[ 21x = 84 \] \[ x = \frac{84}{21} = 4 \] Thus, the equation that would be used is 21x + 42 = 126.
Finally, let's summarize the answers you needed:
- 15
- 9
- addition and division
- subtraction and division
- 21x + 42 = 126
1 answer