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? \\(\boldsymbol{\frac{70}{100}}\\) shows 70% as a ratio. the ratio \\(\boldsymbol{\frac{84}{x}}\\) compares 84 to the whole, x. a these ratios must be equal, so write an equation and solve for x: x = 120. \\(\boldsymbol{\frac{70}{100}}\\) shows 70% as a ratio. the ratio \\(\boldsymbol{\frac{84}{x}}\\) compares 84 to the whole, x. b multiply these ratios to find x: x = 58.8. \\(\boldsymbol{\frac{70}{100}}\\) shows 70% as a ratio. the ratio \\(\boldsymbol{\frac{x}{84}}\\) compares 84 to the whole, x. c these ratios must be equal, so write an equation and solve for x: x = 58.8. \\(\boldsymbol{\frac{70}{100}}\\) shows 70% as a ratio. the ratio \\(\boldsymbol{\frac{x}{84}}\\) compares 84 to the whole, x. d multiply these ratios to find x: x = 120.

Explanation:

Question 1

A percent represents a constant of proportionality (since it's a fixed ratio) that describes the part of the whole. So the correct words are "constant", "part", "whole".

Step1: Identify the first blank

A percent is a constant of proportionality (as it's a fixed ratio between part and whole). So first blank: constant.

Step2: Identify the second blank

It describes the part (the portion) of the whole. So second blank: part.

Step3: Identify the third blank

The part is of the whole. So third blank: whole.

We need to calculate the total fabric bought by Jessica and Derek, then compare.

Step1: Calculate Jessica's fabric

Jessica bought 5 yards plus 20% extra. 20% of 5 is \(0.2\times5 = 1\). So total for Jessica: \(5 + 1=6\) yards.

Step2: Calculate Derek's fabric

Derek bought 3 yards plus 25% extra. 25% of 3 is \(0.25\times3 = 0.75\). So total for Derek: \(3+ 0.75 = 3.75\) yards.

Step3: Compare and find the difference

Jessica bought more. Difference: \(6 - 3.75=2.25\) yards.

Calculate the number of rings Lou sold, then compare with Jacob's.

Step1: Calculate Lou's rings

Lou sold 200 pieces, 20% were rings. \(20\%\text{ of }200 = 0.2\times200 = 40\) rings.

Step2: Compare with Jacob's rings

Jacob sold 35 rings. Lou sold more. Difference: \(40 - 35 = 5\) rings.

Answer:

A percent is a \(\boldsymbol{\text{constant}}\) of proportionality describing the \(\boldsymbol{\text{part}}\) of the \(\boldsymbol{\text{whole}}\).

Question 2