1. John is filling a bathtub that is 18 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take ten more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct? Eplain. Water Level (inches) Time (mins) 6 9 12 1 18 2 6 8 10 12 Rate inches: 2 mins Unit Rate 1. inches: 1min Yes, Josh is correct, because in 10 more minutes the tub will reach the ma height of 18 inches. 2. You and your friends go to the movies. The cost of admission is $9.0 per person. Create a table showing the relationship between number of people going to the movies and the total cost of admission. Eplain why the cost of admission is proportional to the amount of people. Cost ($) 9.0 19.00 28.0 8.00 7.0 7.00 # of people 1 2 6 Helpful hints to solve this problem: -Identify the givens and goals. -Identify the rate; inches in 2 minutes -Find the Unit Rate; k = y -Set-up a table to organize the information -Set-up ratios of y to determine proportionality. -If all y ratios are equivalent, then we have a proportional relationship. Yes, the cost is proportional to the amount of people, because each ratio of cost/# of people are all equivalent to $9.0 per 1 person.. Graph the following tables and identify if the two quantities are proportional to each other on the graph. Eplain your thinking. -Proportional Relationships must be a straight line and go through the origin. -Verify set-up ratios, if all ratios are equivalent, it confirms that it s a proportional relationship. 1 = 2 6 = 9 = 12 All ratios simplify to 1 Yes, these two quantities are proportional, because the line is straight and is going through the origin.
. Each school year, the 7th graders who study Life Science participate in a special field trip to the city zoo. In 2010, the school paid $1260 for 8 students to enter the zoo. In 2011, the school paid $100 for 70 students to enter the zoo. In 2012, the school paid $19 for 9 students to enter the zoo. a. Is the price the school pays each year in entrance fees proportional to the number of students entering the zoo? Eplain why or why not. Cost 1260 100 19 # of students 8 70 9 All ratios simplify to $1/1 student admission Yes, all ratios are equivalent, therefore this is a proportional relationship. c. Identify the constant of proportionality and eplain what it means in the contet of this situation. k = 1260 8 = 1 For every 1 person, it costs $1. d. Write an equation for this situation. y = 1 Set-up ratios to identify if they are equivalent. k = y # of students = independent Cost = dependent in contet means to eplain the constant in terms of the cost @ the zoo. Equation: y = k If I know the -value, multiply by k If I know my y-value, divide by k e. What would the school pay if 120 students entered the zoo? 1(120) = $1800 f. How many students would enter the zoo if the school paid $1,2? 12/1 = 9 students. It cost $ to send 6 packages through a certain shipping company. Consider the number of packages per dollar. a. Find the constant of proportionality for this situation. 6 1.2 packages = $ $1 b. Write an equation to represent the relationship. y = 1.2 6. Suppose that the cost of renting a snowmobile is $7.0 for hours. a. If the c = cost and h = hours, which variable is the dependent variable? Eplain why. Independent= hours, dependent = cost (without hours there is no cost) b. What is the Unit Rate of this situation? 7.0 = k = $7.0 1 hour When it says per dollar we want our denominator to represent money. k = y Equation: y = k Independent = doesn t rely on the other value Dependent = relies on the independent value k = y = Unit Rate c. Write an equation to represent the relationship. c = 7.h OR y = 7. d. What would be the cost of renting 2 snow mobiles for hours each? 7.0 2 = $7.00 OR (7. ) 2 = $7.00
7. If ¾ lb. of candy cost $20.0, how much would 1 lb. of candy cost? $20. 0 lb $27. = 1 lb Need to find for 1 pound Reminder: anything divided by itself is 1. One pound of candy will cost $27.. 8. The table below shows the combination of dry prepackaged mi and water to make concrete. The mi says for every 1 gallon of water stir 60 pounds of dry mi. We know that 1 gallon of water is equal to 8 pounds. Using the information provided in the table, complete the remaining parts of the table. Find the unit rate of mi/water If I know my water multiply by the constant. If I know my mi, divide by the constant. 60 68 8 When given only the total, find a new unit rate of total/water. 12 1 2 1 2 1 10 When dividing fractions, change to improper fractions, with common denominators. Mi/Water = 7. dry mi/ 1 pound of water Total/water= 8. total pounds/1 pound of water 9. Mark bought an electronic tablet on sale for ¼ off its original price of $82.00. He also wanted to use a coupon for a 1 off the sales price. Before taes, how much did Mark pay for the tablet? 206.2 206.2 206.2 206.2 $82 $82 $206.2 = $618.7 $618.7 - $12.7 = $9.00 The final cost of the tablet is $9.00. 12.7 12.7 12.7 12.7 12.7 $618.7 10. Hayden likes building radio-controlled sailboats with her father. One of the sails, shaped like a right triangle, has side lengths measuring 6 inches, 8 inches and 10 inches. To log her activity, Hayden creates and collects drawings of all the boats she and her father built together. Using the scale factor of 1/, draw a scale drawing of sail. 6 in. 8 in. 10 in. 6 1 1 = 6 = 1 1 2 in. 8 1 1 = 8 = 2 in. 10 1 1 = 10 = 2 1 2 in. 1 1 2 in. 2 in. 2 1 2 in. This questions has two parts First, do ¼ off the original price, then 1/ off the new sale price. ¼ off means I need to divide the original price into equal sections and remove one. 1/ of sale price, take your new sale price and divide it into equal sections and remove one. Draw a picture. Scale Factor: if greater than 1, it s an enlargement; if less than 1, it s a reduction. Multiply each length by the scale factor.
1 inch Cranberry Juice (cups) Name: Period: Date: 11. Students are responsible for providing snacks and drinks for the Junior Beta Club Induction Reception. Susan and Myra were asked to provide the punch for the 100 students and family members who will attend the event. The chart below will help Susan and Myra determine the proportion of cranberry juice to sparkling water that will be needed to make the punch. Complete the chart, graph the data, and write the equation that models this proportional relationship. Sparkling water (cups) Cranberry juice (cups) 1 / 8 6. 12 9 / Drinks for Beta Club k = y = Unit Rate Cranberry/Water If I know my -value, multiply by the constant to find y. If I know my y- value, divide by the constant to find. Equation: y = k (k is my constant) Graphing: intervals need to be consistent. Should show a straight line, going through the origin (proportional) Be sure to label your ais and title the graph. 0 0 100 80 Sparkling Water (cups) Equation: 12. The portrait company that takes little league baseball team photos is offering an option where a portrait of your baseball pose can be enlarged to be used as a wall decal (sticker). Your height in the portrait measures ½ inches. If the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal. Your actual height is inches. If you stand net to the wall decal, will it be larger or smaller than you? Scale Factor: 20 y = 1. On the mall floor plan, 1 inch represents feet in the actual store. What would be the area of the actual store? The scale drawing of the store is below. 2 inches Store. in. Area of drawing: 2 1 = 2 in 2 Method 2: 1 in = 12 ft (actual length) 2 inch = 2 ft (actual length) Actual area: 12 2 = 288 ft 2 Unit Rate: cranberry/1 water Given scale: 1 inch = 20 inches Portrait 1 2. Height (in) Decal Height (in) 20 0 60 70 His decal will be 70 inches; which is 1 inches taller than his actual height. Scale: ¼ inch = ft (6 inches) Method 1: Scale Factor: 6 1 = 1 Square the scale factor: 1 2 = 20,76 Real area (actual area multiplied by the scale factor square): 2 20,76= 1,72 in 2 Convert back to feet (divide by a square foot (1 in 2 ): 1,72/1 = 288 ft 2. If different units, convert-this problem is ok. Set up a table Draw a picture Scale Factor: actual/drawing Multiply drawing lengths by the scale factor. Scale-convert both to inches. Method 1: 1. Find scale factor 2. Square the scale factor. Multiply the squared scale factor by the area of the drawing. Method 2: Convert drawing lengths to actual lengths (in feet), then find the new area.