Name Date Symbolize Problems - Real World Many situations in the real-world can be modeled with a linear equation. When writing an equation based on a real-world situation, consider the following. 1. Initial condition If an initial condition exists in the situation, then this condition will be the y-intercept of the line. 2. Re-occurring condition A re-occurring condition will be a change which happens in the situation on a regular basis and will be the slope of the line. Example 1: At a municipal golf course, it costs each player $32.50 for one round of golf plus $12.50 for the cart fee. If g represents the number of golfers who play one round of golf with a cart, write an equation which represents the total amount of money the golf course will earn from these g golfers. Solution: It costs each golfer $32.50 for one round of golf and $12.50 for the cart fee. So, each golfer pays a total of $45. Therefore, the equation which represents the total amount of money the golf course will earn from g golfers is shown below. p = 45g
Example 2: A concession stand had 250 bags of peanuts when it opened. Each hour, the concession stand sold 50 bags of peanuts. Write an equation which represents the number of bags of peanuts the concession stand had after h hours. Solution: The number of bags of peanuts sold each hour, 50, represents the rate of change. Since the total number of bags of peanuts the concession stand started with decreased by that amount for every hour it was open, and h represents the number of hours it was open, 50 is the value to be attached to the variable h. The total number of bags of peanuts the concession stand sold must be subtracted from the number of bags of peanuts it started with, 250. Therefore, the equation which represents the total number of bags of peanuts after h hours is shown below. b = 250-50h Example 3: The produce manager at Clink's Market bought a crate of artichokes for $21.60. The manager then sold the artichokes for $1.60 each. If n represents the number of artichokes he sold, write an equation which represents the profit he made from selling the artichokes.
Solution: The selling price per artichoke, $1.60, represents the rate of change. Since n represents the number of artichokes sold, $1.60n represents the total money earned from selling n artichokes. To find the profit, the purchase price of the crate must be subtracted from the total money earned. Therefore, the equation which represents the profit the manager made from selling n artichokes is shown below. p = 1.6n - 21.6 Complete the following Real World Problems Multi-Step Real World Problems 1. Carl, Gilda, Conroy, and Kyla are the four candidates in a school election. Carl received of the votes, Gilda received 15% of the votes, and Conroy received of the votes. If Kyla received all of the remaining votes, what percentage of the votes did she receive? A. 50% B. 15% C. 45% D. 40%
2. Mike put 220 baseballs into 10 trash bins. He put the same number of baseballs in each bin. He took 4 trash bins of baseballs to the baseball field. How many baseballs did Mike take? A. 66 B. 480 C. 88 D. 95 3. Kenneth drove 170.85 miles in hours. What was his average speed? A. 57 mph B. 53 mph C. 46 mph D. 51 mph 4. Antonia bought a set of dishes, a towel, and a candle at a housewares store. The set of dishes cost $35.42, the towel cost $21.53, and the candle cost $9.19 before any coupons or discounts. She used a $0.50-off coupon on the candle, a $2.75-off coupon on the towel, and the set of dishes was on sale for 10% off the regular price. Which of the following best describes the amounts that Antonia saved? A. She saved the greatest percentage on the candle. B. She saved the same percentage on the towel and the set of dishes. C. She saved the greatest percentage on the set of dishes. D. She saved the greatest percentage on the towel.
5. Workers Inc. just bought 9 boxes of pens to put in their storage room for employees to use as needed. Each box contains 45 pens. If each of the 30 employees working for Workers Inc. takes 3 pens when they are first brought into the office, how many pens will be left in the storage room? A. 375 B. 315 C. 135 D. 402 6. Joey is putting all of his trophies onto 6 shelves. If he places 7 trophies on each shelf but still has 2 trophies left over, how many trophies does he have? A. 19 B. 44 C. 15 D. 42 7. The temperature outside changed from 64 F to 40 F over a period of six days. If the temperature changed by the same amount each day, what was the daily temperature change? A. 4 F B. -24 F C. 24 F D. -4 F
8. A rectangular cake has a length of inches and a width of inches. How many whole, square pieces of cake with side lengths of from the cake? inches can be cut A. 38 B. 37 C. 36 D. 34 9. Lance baked a pie. Justin ate of the pie, and Joey ate of the pie. How much of the pie is left? A. B. C. D. 10. Rita earns $17.00 per hour. If she gets a 4% raise, what will be her new hourly wage? A. $21.00 B. $16.32 C. $17.68 D. $17.04