fm.1 extra practice

1. estimate, then calculate the unit price of each product.
a) $5.99 for 8 hamburgers
b) $11.96 for 4 containers of windshield washer fluid
c) $1.74 for 4 green peppers
d) $4.77 for 6 rolls of paper towels

2. the unit price of brown sugar in bulk is $1.90 per kilogram. what is the cost of each amount?
a) 5 kg
b) 20 kg
c) 42 kg
d) 0.5 kg

3. given the unit price of each item at a bulk food store, estimate, then calculate the cost of each amount.
\begin{tabular}{|l|c|c|}
\hline
product & unit price & amount \\
\hline
a) raisins & \$0.55/100 g & 500 g \\
\hline
b) pistachios & \$2.05/100 g & 125 g \\
\hline
c) egg noodles & \$0.43/100 g & 275 g \\
\hline
d) tea & \$0.13/10 bags & 75 bags \\
\hline
\end{tabular}

4. a case of 24 juice packs costs $11.97. an 8-pack of juice costs $4.47. which size would be the most economical if you needed to buy 100 drinks for a school breakfast program? explain your thinking.

5. determine the unit price for each item.
a) $7.00 for 400 g of almonds
b) 227 g of mushrooms for $2.99
c) $1.49 for 3.2 kg of tangerines
d) 1.5 kg of pork ribs for $6.68

6. what is the original unit price and the new unit price of each item?
a) 25 kg of potatoes are reduced from $4.99 to $2.99
b) a pack of 8 batteries goes up from $3.49 to $3.99
c) 750 ml of soda for $1.79 goes on sale for $0.79

7. what is the percent increase or decrease in price for each item in #6? round your answers to the nearest percent.

8. determine the unit price using either 1 ml or 1 l. explain your choice.
a) $8.96 for 950 ml of conditioner
b) 50 ml of moisturizer for $16.99
c) 3.7 l of paint for $25.99

Question

fm.1 extra practice

1. estimate, then calculate the unit price of each product.
a) $5.99 for 8 hamburgers
b) $11.96 for 4 containers of windshield washer fluid
c) $1.74 for 4 green peppers
d) $4.77 for 6 rolls of paper towels

2. the unit price of brown sugar in bulk is $1.90 per kilogram. what is the cost of each amount?
a) 5 kg
b) 20 kg
c) 42 kg
d) 0.5 kg

3. given the unit price of each item at a bulk food store, estimate, then calculate the cost of each amount.
\begin{tabular}{|l|c|c|}
\hline
product & unit price & amount \\
\hline
a) raisins & \$0.55/100 g & 500 g \\
\hline
b) pistachios & \$2.05/100 g & 125 g \\
\hline
c) egg noodles & \$0.43/100 g & 275 g \\
\hline
d) tea & \$0.13/10 bags & 75 bags \\
\hline
\end{tabular}

4. a case of 24 juice packs costs $11.97. an 8-pack of juice costs $4.47. which size would be the most economical if you needed to buy 100 drinks for a school breakfast program? explain your thinking.

5. determine the unit price for each item.
a) $7.00 for 400 g of almonds
b) 227 g of mushrooms for $2.99
c) $1.49 for 3.2 kg of tangerines
d) 1.5 kg of pork ribs for $6.68

6. what is the original unit price and the new unit price of each item?
a) 25 kg of potatoes are reduced from $4.99 to $2.99
b) a pack of 8 batteries goes up from $3.49 to $3.99
c) 750 ml of soda for $1.79 goes on sale for $0.79

7. what is the percent increase or decrease in price for each item in #6? round your answers to the nearest percent.

8. determine the unit price using either 1 ml or 1 l. explain your choice.
a) $8.96 for 950 ml of conditioner
b) 50 ml of moisturizer for $16.99
c) 3.7 l of paint for $25.99

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Unit Price", "Percent Change", "Rate and Proportion" ], "current_concepts": [ "Linear Equations", "Unit Price", "Percent Change", "Rate and Proportion" ] } ## Calculate unit prices for Question 1 Using the **Linear Equations** knowledge point, we divide the total cost by the quantity to find the unit price. a) Estimate: $ \$6.00 \div 8 = \$0.75 $ per hamburger. Calculation: $ \$5.99 \div 8 \approx \$0.75 $ per hamburger. b) Estimate: $ \$12.00 \div 4 = \$3.00 $ per container. Calculation: $ \$11.96 \div 4 = \$2.99 $ per container. c) Estimate: $ \$1.80 \div 4 = \$0.45 $ per green pepper. Calculation: $ \$1.74 \div 4 \approx \$0.44 $ per green pepper. d) Estimate: $ \$4.80 \div 6 = \$0.80 $ per roll. Calculation: $ \$4.77 \div 6 \approx \$0.80 $ per roll. ## Calculate costs for Question 2 Using the **Linear Equations** knowledge point, we multiply the unit price of $ \$1.90/\text{kg} $ by each mass. a) $ 5\text{ kg} \times \$1.90/\text{kg} = \$9.50 $ b) $ 20\text{ kg} \times \$1.90/\text{kg} = \$38.00 $ c) $ 42\text{ kg} \times \$1.90/\text{kg} = \$79.80 $ d) $ 0.5\text{ kg} \times \$1.90/\text{kg} = \$0.95 $ ## Calculate costs for Question 3 Using the **Linear Equations** knowledge point, we scale the unit prices to the given amounts. a) Raisins: $ 500\text{ g} $ is $ 5 \times 100\text{ g} $. Estimate: $ 5 \times \$0.60 = \$3.00 $. Calculation: $ 5 \times \$0.55 = \$2.75 $. b) Pistachios: $ 125\text{ g} $ is $ 1.25 \times 100\text{ g} $. Estimate: $ 1.25 \times \$2.00 = \$2.50 $. Calculation: $ 1.25 \times \$2.05 \approx \$2.56 $. c) Egg noodles: $ 275\text{ g} $ is $ 2.75 \times 100\text{ g} $. Estimate: $ 3 \times \$0.40 = \$1.20 $. Calculation: $ 2.75 \times \$0.43 \approx \$1.18 $. d) Tea: $ 75\text{ bags} $ is $ 7.5 \times 10\text{ bags} $. Estimate: $ 7.5 \times \$0.10 = \$0.75 $. Calculation: $ 7.5 \times \$0.13 \approx \$0.98 $. ## Compare juice pack economy for Question 4 Using the **Linear Equations** knowledge point, we find the cost to buy exactly 100 drinks. - Case of 24: To get 100 drinks, we need $ \lceil 100 \div 24 ceil = 5 $ cases (120 drinks). Cost: $ 5 \times \$11.97 = \$59.85 $. Unit price: $ \$11.97 \div 24 \approx \$0.50 $ per pack. - Pack of 8: To get 100 drinks, we need $ \lceil 100 \div 8 ceil = 13 $ packs (104 drinks). Cost: $ 13 \times \$4.47 = \$58.11 $. Unit price: $ \$4.47 \div 8 \approx \$0.56 $ per pack. Even though the 24-pack has a lower unit price ($ \$0.50 $ vs $ \$0.56 $), buying thirteen 8-packs is cheaper overall ($ \$58.11 $ vs $ \$59.85 $) because it minimizes excess leftover drinks. ## Calculate unit prices for Question 5 Using the **Linear Equations** knowledge point, we calculate the unit prices. a) $ \$7.00 \div 400\text{ g} = \$0.0175/\text{g} $ (or $ \$1.75/100\text{ g} $). b) $ \$2.99 \div 227\text{ g} \approx \$0.0132/\text{g} $ (or $ \$1.32/100\text{ g} $). c) $ \$1.49 \div 3.2\text{ kg} \approx \$0.47/\text{kg} $. d) $ \$6.68 \div 1.5\text{ kg} \approx \$4.45/\text{kg} $. ## Determine original and new unit prices for Question 6 Using the **Linear Equations** knowledge point, we find the unit rates before and after. a) Original: $ \$4.99 \div 25\text{ kg} \approx \$0.20/\text{kg} $. New: $ \$2.99 \div 25\text{ kg} \approx \$0.12/\text{kg} $. b) Original: $ \$3.49 \div 8 \approx \$0.44/\text{battery} $. New: $ \$3.99 \div 8 \approx \$0.50/\text{battery} $. c) Original: $ \$1.79 \div 750\text{ mL} \approx \$0.0024/\text{mL} $ (or $ \$0.24/100\text{ mL} $). New: $ \$0.79 \div 750\text{ mL} \approx \$0.0011/\text{mL} $ (or $ \$0.11/100\text{ mL} $). ## Calculate percent changes for Question 7 Using the **Linear Equations** knowledge point, we find the percent change using $ \frac{\text{New Price} - \text{Original Price}}{\text{Original Price}} \times 100\% $. a) $ \frac{2.99 - 4.99}{4.99} \times 100\% \approx -40\% $ (40% decrease). b) $ \frac{3.99 - 3.49}{3.49} \times 100\% \approx +14\% $ (14% increase). c) $ \frac{0.79 - 1.79}{1.79} \times 100\% \approx -56\% $ (56% decrease). ## Determine unit prices with appropriate units for Question 8 Using the **Linear Equations** knowledge point, we choose the unit that avoids extremely small decimals. a) Use 1 L because 950 mL is close to 1 L. $ 950\text{ mL} = 0.95\text{ L} $. Unit price: $ \$8.96 \div 0.95\text{ L} \approx \$9.43/\text{L} $. b) Use 1 mL because 50 mL is a very small volume. Unit price: $ \$16.99 \div 50\text{ mL} \approx \$0.34/\text{mL} $. c) Use 1 L because 3.7 L is a larger volume. Unit price: $ \$25.99 \div 3.7\text{ L} \approx \$7.02/\text{L} $. ## Question 1 a) Estimate: $ \$0.75/\text{hamburger} $, Calculation: $ \$0.75/\text{hamburger} $ b) Estimate: $ \$3.00/\text{container} $, Calculation: $ \$2.99/\text{container} $ c) Estimate: $ \$0.45/\text{pepper} $, Calculation: $ \$0.44/\text{pepper} $ d) Estimate: $ \$0.80/\text{roll} $, Calculation: $ \$0.80/\text{roll} $ ## Question 2 a) $ \$9.50 $ b) $ \$38.00 $ c) $ \$79.80 $ d) $ \$0.95 $ ## Question 3 a) Estimate: $ \$3.00 $, Calculation: $ \$2.75 $ b) Estimate: $ \$2.50 $, Calculation: $ \$2.56 $ c) Estimate: $ \$1.20 $, Calculation: $ \$1.18 $ d) Estimate: $ \$0.75 $, Calculation: $ \$0.98 $ ## Question 4 The 8-pack is more economical. Buying thirteen 8-packs costs $ \$58.11 $ (104 drinks), whereas buying five 24-packs costs $ \$59.85 $ (120 drinks). ## Question 5 a) $ \$1.75/100\text{ g} $ (or $ \$0.0175/\text{g} $) b) $ \$1.32/100\text{ g} $ (or $ \$0.0132/\text{g} $) c) $ \$0.47/\text{kg} $ d) $ \$4.45/\text{kg} $ ## Question 6 a) Original: $ \$0.20/\text{kg} $, New: $ \$0.12/\text{kg} $ b) Original: $ \$0.44/\text{battery} $, New: $ \$0.50/\text{battery} $ c) Original: $ \$0.24/100\text{ mL} $, New: $ \$0.11/100\text{ mL} $ ## Question 7 a) $ 40\% $ decrease b) $ 14\% $ increase c) $ 56\% $ decrease ## Question 8 a) 1 L; $ \$9.43/\text{L} $ (950 mL is close to 1 L, making 1 L a practical unit) b) 1 mL; $ \$0.34/\text{mL} $ (50 mL is a very small package, so 1 mL is more appropriate) c) 1 L; $ \$7.02/\text{L} $ (3.7 L is a large volume, making 1 L a practical unit) { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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Question

Explanation:

Calculate unit prices for Question 1

Calculate costs for Question 2

Calculate costs for Question 3

Compare juice pack economy for Question 4

Calculate unit prices for Question 5

Determine original and new unit prices for Question 6

Answer:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8