Garden Planning Your Assignment: Your neighbor, John, is building a tomato garden for his mother. Use your knowledge of rational numbers, ratios, and geometry to help John during his project. Copyright 2016 Key Data Systems 1
Part A: 1. John decides to begin his gardening project by purchasing bags of soil to spread in the new garden. The hardware store sells two different types of soil. Each bag of Brand A has a volume of 2 cubic yards and sells for $6.45 each, and each bag of Brand B has a volume of 3 cubic yards and sells for $7.09 each. He buys a total of 4 bags of Brand A and 2 bags of Brand B. After John is finished spreading the soil in his garden, he realizes he has used only 3 of the total amount of soil he bought. 4 Enter the mixed number that represents the total number of cubic feet of soil John has left over? feet 3 2. John also needs to purchase fertilizer for the new garden, and he finds two types at the store. One bag of Brand A costs $4.12 and weighs 5.5 pounds, and one bag of Brand B costs 72% more than Brand A and weighs 81% more than Brand A. John needs to buy at least 30 pounds of fertilizer. What combination of fertilizer brands will give him the correct weight at the lowest price? A. 2 bags of Brand A and 3 bags of Brand B B. 4 bags of Brand A and 1 bag of Brand B C. 1 bag of Brand A and 4 bags of Brand B D. 5 bags of brand A and no bags of Brand B Copyright 2016 Key Data Systems 2
Part B: 3. John's mother told him that she would like a garden in the shape of a triangle, which can be represented by Triangle ABC. His mother has also given him some measurement guidelines of the garden, which can be found below: Line segment AB has a length of 5.596 feet. Line segment BC has a length of 8.416 feet. Line segment AC has a length of 10.11 feet. Angle BAC measures 56.38. Angle ACB measures 33.62. Using your knowledge of interior angles of triangles, explain the equation John can use to calculate the area of the triangle, rounded to the nearest thousandth. Include the measurement of Angle ABC in your response. Copyright 2016 Key Data Systems 3
4. John's mother has chosen to plant tomatoes in her new garden. Tomato plants are sold in triangular-shaped containers. Yellow tomatoes are sold in containers with a base area of 20.36 in². Red tomatoes are sold in a 2.5-inch tall container with the following base: John's mother wants to plant as many tomato plants as possible in her garden. If no plants will overlap each other, which type of tomato plant should she choose? Using your answer from the previous question, what is the maximum number of that type of plant that will fit in the garden? Explain your reasoning. Copyright 2016 Key Data Systems 4
5. John is now ready to plant the tomato plants in the garden. He knows that he will work at a constant rate of 7.5 minutes for every 5 plants planted. John creates this proportion to calculate the total time, in minutes, it will take him to finish planting the number of tomato plants calculated in Question 4: 7.5 minutes 5 plants = 60 minutes x plants Did John create an accurate proportion to determine the total time? If he did, finish calculating the proportion. If he did not create an accurate proportion, explain what the mistake is, correct his mistake, and finish calculating the proportion. Copyright 2016 Key Data Systems 5
6. When John originally went shopping for the tomato plants, he was able to buy them in boxes holding 10 plants per box, and he spent a total of $494. When John made the purchase, the store clerk told him that he could return any individual plants left over and get back half the original cost of each plant. He is now finished planting the tomato plants and is calculating the amount he should receive back for the plants that he will return. John calculates that because 494 10 = 49.4, he should receive $49.40 back per plant. What are John's mistakes? Correct his mistakes and calculate the amount back per plant and the total amount back John should receive. Use the maximum number of plants you calculated in Question 4 in your calculations. END OF PERFORMANCE TASK Copyright 2016 Key Data Systems 6