Question

1. fill in the blanks with the provided words to explain how the percent relates proportional quantities. variable part whole constant a percent is a __ of proportionality describing the of the __. 2. sewing patterns recommend buying extra fabric in case of mistakes. jessica bought 5 yards of fabric, plus 20% extra fabric. derek bought 3 yards of fabric, plus 25% extra. who bought more fabric? how much more? 3. lou and jacob each sold 200 pieces of jewelry. if 20% of lou’s sales were rings, and jacob sold 35 rings, who sold more rings? how many more? 4. elsie bought a video game for $85.00. if the store charges 170% of what it paid for the game, how much is the store’s profit? 5. fill in the blanks with the correct percent that represents each situation. 33\frac{1}{3}\\% 80% 15% 95% katrina made 4 of her last 5 shots. miguel runs faster than his 19 teammates. what percent of the team is slower than miguel? fifty of 150 students wear school spirit t - shirts. micah saved $6 on a $40 pair of pants. 6. if you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole? a \\(\frac{70}{100}\\) shows 70% as a ratio. the ratio \\(\frac{84}{x}\\) compares 84 to the whole, x. these ratios must be equal, so write an equation and solve for x: x = 120. b \\(\frac{70}{100}\\) shows 70% as a ratio. the ratio \\(\frac{84}{x}\\) compares 84 to the whole, x. multiply these ratios to find x: x = 58.8. c \\(\frac{70}{100}\\) shows 70% as a ratio. the ratio \\(\frac{x}{84}\\) compares 84 to the whole, x. these ratios must be equal, so write an equation and solve for x: x = 58.8. d \\(\frac{70}{100}\\) shows 70% as a ratio. the ratio \\(\frac{x}{84}\\) compares 84 to the whole, x. multiply these ratios to find x: x = 120.

Explanation:

Question 2

Step 1: Calculate Jessica's total fabric

Jessica bought 5 yards, plus 20% extra. 20% of 5 is \( 0.20 \times 5 = 1 \) yard. So total is \( 5 + 1 = 6 \) yards.

Step 2: Calculate Derek's total fabric

Derek bought 3 yards, plus 25% extra. 25% of 3 is \( 0.25 \times 3 = 0.75 \) yards. So total is \( 3 + 0.75 = 3.75 \) yards.

Step 3: Compare and find the difference

Jessica has 6 yards, Derek has 3.75 yards. Jessica bought more. Difference is \( 6 - 3.75 = 2.25 \) yards.

Step 1: Calculate Lou's rings

Lou sold 200 pieces, 20% were rings. \( 0.20 \times 200 = 40 \) rings.

Step 2: Compare with Jacob's rings

Jacob sold 35 rings. Lou sold more.

Step 3: Find the difference

\( 40 - 35 = 5 \) rings.

Step 1: Let the store's cost be \( x \)

The store charges 170% of \( x \), which is $85. So \( 1.70x = 85 \).

Step 2: Solve for \( x \)

\( x = \frac{85}{1.70} = 50 \).

Step 3: Calculate profit

Profit is selling price - cost: \( 85 - 50 = 35 \).

Answer:

Jessica bought more fabric. She bought 2.25 yards more.

Question 3