Question

jeff is planting a vegetable garden. he plants 6 kale, 10 broccoli, 4 tomato, and 5 carrot plants.
a) write the following ratios and reduce them to lowest terms:
kale plants to tomato plants
broccoli to kale to other
carrots to non - carrots
b) write the ratio of tomato plants to total plants as a fraction, decimal, and percent.
kate plays basketball. in one game, she took 8 free throws. she got 6 in and missed 2.
a) write the ratio of made free throws to total free throws as a fraction, decimal, and percent.
b) if she takes 80 free throws in one season, how many do you think she will make?
what assumption are you making?
a lasagna recipe calls for 100 g of romano cheese, 250 g of mozzarella cheese, and 400 g of ricotta cheese.
a) write a ratio in lowest terms to compare the amounts of the 3 cheeses.
b) what is the total amount of cheese required to make a lasagna that contains 900 g of ricotta?
my current proficiency level on this concept is...
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Explanation:

Jeff's Vegetable Garden (a)

Kale plants to tomato plants

Step1: Identify quantities

Kale plants = 6, Tomato plants = 4.

Step2: Write ratio

Ratio: \( 6:4 \).

Step3: Simplify ratio

Divide both by GCD(6,4)=2: \( \frac{6}{2}:\frac{4}{2} = 3:2 \).

Broccoli to kale to other

Step1: Identify "other" plants

Other plants = Tomato + Carrot = 4 + 5 = 9. Broccoli = 10, Kale = 6.

Step2: Write ratio

Ratio: \( 10:6:9 \) (already in lowest terms as GCD(10,6,9)=1).

Carrots to non - carrots

Step1: Identify non - carrot plants

Non - carrot plants = Kale + Broccoli + Tomato = 6 + 10 + 4 = 20. Carrots = 5.

Step2: Write ratio

Ratio: \( 5:20 \).

Step3: Simplify ratio

Divide both by GCD(5,20)=5: \( \frac{5}{5}:\frac{20}{5}=1:4 \).

Jeff's Vegetable Garden (b)

Step1: Calculate total plants

Total plants = 6 (kale) + 10 (broccoli) + 4 (tomato) + 5 (carrot) = 25. Tomato plants = 4.

Step2: Fraction

Ratio as fraction: \( \frac{4}{25} \).

Step3: Decimal

Divide 4 by 25: \( 4\div25 = 0.16 \).

Step4: Percent

Multiply decimal by 100: \( 0.16\times100 = 16\% \).

Kate's Basketball (a)

Step1: Identify quantities

Made free throws = 6, Total free throws = 8.

Step2: Fraction

Ratio as fraction: \( \frac{6}{8}=\frac{3}{4} \) (divided by GCD(6,8)=2).

Step3: Decimal

Divide 3 by 4: \( 3\div4 = 0.75 \).

Step4: Percent

Multiply decimal by 100: \( 0.75\times100 = 75\% \).

Kate's Basketball (b)

Answer:

Step1: Determine multiplier

Ricotta is 800g, original Ricotta = 400g. Multiplier = \( \frac{800}{400}=2 \).

Step2: Calculate other cheeses

Romano = \( 100\times2 = 200 \)g, Mozzarella = \( 250\times2 = 500 \)g.

Step3: Total cheese

Total cheese = 200 + 500 + 800 = 1500g.

Final Answers

Jeff (a)

• Kale to Tomato: \( \boldsymbol{3:2} \)
• Broccoli to Kale to Other: \( \boldsymbol{10:6:9} \)
• Carrots to Non - carrots: \( \boldsymbol{1:4} \)

Jeff (b)

• Fraction: \( \boldsymbol{\frac{4}{25}} \)
• Decimal: \( \boldsymbol{0.16} \)
• Percent: \( \boldsymbol{16\%} \)

Kate (a)

• Fraction: \( \boldsymbol{\frac{3}{4}} \)
• Decimal: \( \boldsymbol{0.75} \)
• Percent: \( \boldsymbol{75\%} \)

Kate (b)

• Made throws: \( \boldsymbol{60} \)
• Assumption: Kate's free - throw success rate remains constant.

Lasagna (a)

• Ratio: \( \boldsymbol{2:5:8} \)

Lasagna (b)

• Total cheese: \( \boldsymbol{1500} \) grams