Unit: Ratios & Proportions Video # 4 Learning Target: I can use proportional relationships to solve application problems.

General Formula Even though each application is slightly different, most can be solved by using the following general formula: *Probability, Percent Change and & Measurement questions cant be solved using this.

Application 1: Discount Discount is an amount that you take off a total (a sale) To find a discount: Set up the proportion Cross multiply & divide Subtract your answer from the original total. Ex: The dress that Ana wants costs $200, but is on sale for 25% off. What is the cost of the dress? The final cost of the dress $150

Application 2: Tax Tax is an extra amount of money that you have to pay for buying pretty much everything! To find tax: Set up the proportion Cross multiply & divide Add the answer to the original total. Ex: After shopping, Ms. Rebecca’s total was $120 dollars. If New York State has 8.5% tax, what is Ms. Rebecca’s total with tax? The total is $132.20 *Notice the difference between discount and tax: discount gets subtracted and tax gets added

Application 3: Tip Tip is extra money you pay when you go out to eat. To Find tip: Set up the proportion Cross multiply & divide Add your answer to the original amount Ex: Shanyah and Adrianna went out to eat at BBQ’s. Their bill came to $85. If they want to leave an 18% tip, how much will their total be with tip? So their total is $100.30

Application 4: Percent Change Percent Change is used when we want to know by what percent a product’s price changed. To find percent change: Subtract the new price from the original price Divide that number by the original price Convert that decimal answer to a percent by moving the decimal 2 places to the right. Joanna wanted a shirt from American Eagle that was $30. It is now on sale for $25. By what percent did the price change? The price decreased by approx. 16.7%

Application 5: Survey Results We will talk about this application more when we do our probability unit, but here is an introduction When we are looking at survey results sometimes they ask us to find the probability for a different total. To do this: Find the probability of what it is they are talking about (part/whole) Set up a proportion with the new total as the second denominator. Solve for the missing numerator. Mya asked 50 students what their favorite sport was. 20 answered basketball. Based on these results, if Mya asks 1,000 students, how many should we expect to answer basketball? We should expect 400 students to answer basketball.

Application 6: Measurement Conversions Sometimes when we are working with different units of measurement, it is easier to convert one unit to another. This can be easily done with a proportion: Set up the given info into a proportion. Make sure things with the same units are in the same spots in the proportion Solve the proportion for the missing piece. Shanice is baking cookies. The recipe calls for 2 quarts of milk, but she only has a measuring cup in pints. If there are 2 pints in a quart, how many pints of milk does Shanice need for the recipe?

Application 7: Rate of Change A rate of change is a rate that describes how one quantity changes in relation to another. To find the rate of change on a table, find the change for each different thing and write the numbers as a fraction If the change is the same for the entire table, the change is called constant To find the rate of change on a graph, find the change in the y values and then the change in your x values. Write the answer as a fraction On a graph, if it is a constant rate of change, the line will be straight Ex: The table shows the amount of money a booster club makes washing cars for a fundraiser. Use the information to find the constant rate of change in dollars per car. Change in money = 40 dollars Change in cars = 5 cars Change = $8/1 car The number of dollars earned increases by $8 for every car washed. Cars Washed Number Money ($) 5 40 10 80 15 120 20 160 *A constant rate of change can also be called a direct variation!!!

Application 8: Slope In a linear relationship, the vertical change (change in the y-value) per unit of horizontal change (change in x-value) is always the same. The ratio is called the slope of the function This is the same as constant rate of change! The slope tells you how steep a line is. The vertical change is called the rise and the horizontal change is called the run so slope = rise/run Ex: The table below shows the relationship between the number of seconds, y, it takes to hear thunder after lightning strike and the miles x you are from the lightning. Find the slope. Change in y (seconds) = 5 Change in x (miles) = 1 Slope = 5/1 So for every 5 seconds between a lightning flash and the sound of thunder, there is 1 mile between you and the lightning strike Miles (x) Seconds (y) 1 5 2 10 3 15 4 20 25 *Slope is always written as a fraction!!!!

Application 9: Simple Interest Simple interest is money that you earn for putting your money in the bank or lending your money to be borrowed. This is the same as constant rate of change! To find simple interest use the formula: I = p*r*t I = interest P = Principal (which is the amount of money you deposit or loan) R = rate of interest (always change percent into a decimal) T = amount of time money is in bank or borrowed (usually in years) Ex: Arnold puts $580 into a savings account. The account pays 3% simple interest. How much interest will he earn in 5 years? I = p*r*t I = (580)(.03)(5) I = $87 *If the amount of time is in months, convert it to years *Always convert rate into a decimal!!