Sure, let's break it down step by step.
### Mia's Shelter
1. **Finding the Length Board:**
- Mia wants a length of 3.25 feet.
- Convert 3.25 feet to inches: \( 3.25 \times 12 = 39 \) inches.
- So, Mia will use the 39-inch board for the length.
2. **Width of the Shelter:**
- The width has to be shorter than the length. So, it will either be 36 inches or 42 inches.
- Convert 36 and 42 inches to feet:
- \( 36 \text{ inches} = \frac{36}{12} = 3 \text{ feet} \)
- \( 42 \text{ inches} = \frac{42}{12} = 3.5 \text{ feet} \)
- Since the width must be shorter than the length (3.25 feet), the width will be 3 feet (36 inches).
3. **Cutting the Third Board:**
- Mia has the 42-inch board left.
- She needs to cut it to match the width (3 feet = 36 inches).
- The length to cut off is \( 42 - 36 = 6 \) inches.
- Convert 6 inches to feet: \( \frac{6}{12} = 0.5 \) feet.
- Mia needs to cut off 0.5 feet from the 42-inch board.
4. **Roof Boards:**
- Convert each measurement to square feet to compare:
- 1 square yard: \( 1 \text{ yd}^2 = 9 \text{ ft}^2 \).
- \( 3 \text{ ft} \times 3 \text{ ft} = 9 \text{ ft}^2 \).
- \( 36 \text{ in} \times 36 \text{ in} = 1296 \text{ in}^2 \). Convert square inches to square feet: \( 1296 \text{ in}^2 = \frac{1296}{144} = 9 \text{ ft}^2 \).
- All three boards measure the same area, so any board will cover the space needed for the roof.
### Roger's Punch
1. **Converting Quantities to Liters:**
- 2 quarts of orange juice: \( 2 \times 1.06 = 2.12 \) liters.
- 3 cups of cranberry juice: \( 3 \div 4.23 = 0.7 \) liters.
- 1 gallon of ginger ale: \( 1 \times 3.78 = 3.78 \) liters.
- 1 pint of pineapple juice: \( 1 \times 0.473 = 0.47 \) liters.
- Total: \( 2.12 + 0.7 + 3.78 + 0.47 = 7.07 \) liters.
- Since 8 liters is the bowl's capacity and 7.07 liters is the total liquid, he can use the bowl and can fit \( 8 - 7.07 = 0.93 \) more liters.
2. **Turkey vs. Cheese:**
- 2.25 pounds of cheese: \( 2.25 \div 2.2 = 1.02 \) kilograms.
- Comparing:
- Turkey: 1.5 kilograms.
- Cheese: 1.02 kilograms.
- Therefore, Roger bought more turkey than cheese.
3. **Amount of Chicken:**
- Beef: 1.25 kilograms.
- Turkey: 1.5 kilograms.
- Chicken must be > 1.25 kg and < 1.5 kg.
- Convert to pounds:
- 1.25 kg = 2.75 pounds.
- 1.5 kg = 3.3 pounds.
- Therefore, the chicken could weigh, for example, 3.00 pounds (\( 3 \) pounds lies between 2.75 and 3.3 pounds).
4. **Total Weight in Ounces vs. Grams:**
- Turkey: \( 1.5 \times 2.2 = 3.3 \) pounds = \( 3.3 \times 16 = 52.8 \) ounces.
- Beef: \( 1.25 \times 2.2 = 2.75 \) pounds = \( 2.75 \times 16 = 44 \) ounces.
- Cheese: \( 2.25 \) pounds = \( 2.25 \times 16 = 36 \) ounces.
- Chicken: 3.00 pounds = \( 3 \times 16 = 48 \) ounces.
- Total in ounces: \( 52.8 + 44 + 36 + 48 = 180.8 \) ounces.
- Total in grams: \( 1.5 \times 1000 + 1.25 \times 1000 + 1.02 \times 1000 + 1.36 \times 1000 = 5000 \) grams.
- Since 5000 grams > 180.8 ounces, the total weight in grams is greater than in ounces.
### Sales Tax Calculation
1. **Determine Cost:**
- Let's assume the board game costs $15.75 in Vermont.
- Vermont's general sales tax rate: 6%.
- Total cost: \( 15.75 \times 1.06 = 16.695 \approx \) $16.70.
### Li's Personal Finance:
1. **Monthly Savings:**
- Monthly earnings: \( 30 \times 4 = 120 \) dollars.
- Monthly savings: \( 120 \times 0.60 = 72 \) dollars.
- Li deposits $72 each month.
2. **Value of CD After One Year:**
- Initial amount: $250.
- Annual interest: \( 250 \times 0.026 = 6.50 \) dollars.
- Total value after one year: \( 250 + 6.50 = 256.50 \) dollars.
3. **Cost of Skateboarding Set:**
- Original price: $54.99.
- Sale price: \( 54.99 \times 0.70 = 38.493 \approx 38.49 \) dollars.
- Additional discount: \( 38.49 \times 0.90 = 34.641 \approx 34.64 \) dollars.
- Sales tax: \( 34.64 \times 1.0575 = 36.62 \) dollars.
- Total cost needed: $36.62.
Use what you have learned about converting within a system of measurements to answer the following questions. Mia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants. Answer the following questions. Show your work. Mia will use one of these boards for the length of the shelter. She knows she wants the length of the shelter to measure 3.25 feet. She will use a different board for the width of the shelter. The width of the shelter will be shorter than the length. Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches? What is the width of the shelter, measured in feet? Mia needs to cut the third board to match the width of the shelter. How many feet of board will she need to cut off the existing board to reach this goal? For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. 1 ft. = 1/3 yard. Which of the boards, if any, will cover all the space needed for the roof? Explain your answer, drawing a picture as necessary. Converting Between Systems Use what you have learned about converting between metric and imperial measurements to answer the following questions. Roger is planning a party. He needs these ingredients in the following quantities to make punch: 2 quarts orange juice 3 cups cranberry juice 1 gallon ginger ale 1 pint pineapple juice Roger knows he will need a relatively large container to mix the punch. Unfortunately, all he can find is a bowl that holds 8 liters of liquid. He is not sure whether he can fit all the ingredients in the bowl at the same time. Use the following measurement equivalents to determine whether Roger can use the 8-liter bowl to mix all the ingredients for the punch. 1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons. Show your work. If Roger can use the bowl, he needs to determine how many liters of liquid could still fit into the bowl. If he cannot use the bowl, he needs to determine how many extra liters of liquid there are. Round your answers to the nearest tenth of a liter. Show your work. Roger also wants to make sandwiches for his guests. He buys the following sandwich fillings: 1.5 kilograms of turkey 1.25 kilograms of beef 2.25 pounds of cheese Roger wants to know whether he purchased more turkey or more cheese. Use the conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer. Show your work. Roger discovers that he needs to buy some chicken as well. He buys an amount of chicken that weighs more than the beef he bought and less than the turkey he bought. Give an amount in pounds that the chicken could weigh, rounded to the nearest hundredth of a pound. Show your work. Roger is curious to know the total weight of all four sandwich fillings he bought. He weighs the fillings twice, once using ounces and once using grams. If 16 ounces = 1 pound and 1,000 grams = 1 kilogram, will the total weight of the sandwich fillings be a greater number of ounces or a greater number of grams? Explain your answer. Calculating Sales Tax Use what you have learned about using proportional relationships to answer the following questions. You are visiting one of the following states: Tennessee, Vermont, Wisconsin, or Wyoming. Each has a state sales tax on most items that are for sale in stores. While you are visiting, you decide to buy a board game to play with your hosts. The cost of the game is between $10 and $20, and it is not a whole dollar amount. Decide the cost of the board game. Choose one of the four states: Tennessee, Vermont, Wisconsin, or Wyoming. Research to find your chosen state’s general sales tax. Note, some counties, towns, or cities may add more to the general sales tax, but you only need the general sales tax. What is the total cost of the board game, including sales tax? Show your work. Solving Personal Finance Percentage Problems Use what you have learned about solving percentage problems involving personal finance to answer the following questions. Li earns $30 each week mowing lawns in her neighborhood. She puts 60% of her earnings into her savings account at the end of each month. How much money does Li deposit into her account each month? Show your work. After saving $250, Li invests in a certificate of deposit (CD) that pays 2.6% annual interest. What will be the value of Li’s CD after she has had it for one year? Show your work. Li wants to buy a skateboarding helmet and pads. She sees a set she likes at a sporting goods store. The set costs $54.99. It is on sale for 30% off. Li has a coupon that will take an additional 10% off the sale price. She lives in a state that charges 5.75% sales tax. How much will Li have to earn to pay for the skateboarding set? Show your work.
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