1.3 Problem-Solving Procedures 21 Example 1 Ordering Tacos Zola is purchasing tacos for the 21 members of the debate club. She collects money from members and receives $93. Taco Bueno sells two different boxes of tacos. The small box contains 8 tacos for $10 and the large box contains 12 tacos for $14. The tacos are all the same size, and she must order whole boxes. a) What is the maximum number of tacos that Zola can order for $93 or less? b) If the maximum number of tacos is purchased in the most economical way, how much will the tacos cost? Solution a) We may need to read the problem several times until we understand the facts given and what we are asked to determine. Next, we make a list of the given facts and determine which facts are relevant to answering the question asked. GIVEN INFORMATION Person ordering: Zola Group of people: debate club Number of members: 21 Amount of money collected: $93 Restaurant: Taco Bueno Small box contains 8 tacos Small box costs $10 Large box contains 12 tacos Large box costs $14 Tacos are all the same size Only whole boxes can be purchased We need to determine the maximum number of tacos Zola can purchase for the money collected. To determine this number, we need to know the amount of money collected, the number of tacos in each box, and the cost of each box. We also need to know that only whole boxes can be purchased. RELEVANT INFORMATION Amount of money collected: $93 Small box contains 8 tacos Small box costs $10 Large box contains 12 tacos Large box costs $14 Only whole boxes can be purchased We need a plan to determine the maximum number of tacos that can be purchased for $93 or less. One method is to set up a table to compare the costs of different combinations of the boxes. We can start by determining the maximum number of large boxes that can be purchased. Then reduce the number of large boxes and add more small boxes. In each case, we need to keep the cost at $93 or less. We can determine the maximum number of large boxes that can be purchased by dividing the amount collected, $93, by the price of a large box of tacos, $14: $93 $14 ÷ is approximately 6.6. Since only whole boxes can be purchased, 6 large boxes can be purchased. The price of 6 large boxes is 6 $14 $84. × = Since a small box costs $10, there is not enough money left over to purchase any small boxes. The 6 large boxes of tacos would have 6 12 × or 72 tacos. This first option is shown in the first row of the following table. Other options shown in the table are determined by reducing the number of large boxes and then adding small boxes while keeping the total cost at or below $93. How many ostriches must replace the question mark to balance the fourth scale? Assume that all animals of the same kind have the same weight. That is, all giraffes weigh the same, and so forth. The answer is upside down below. RECREATIONAL MATH Ostriches 0 0 0 0 ? 0 0 0 0 Answer: 3 ostriches
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