TEKS 7.6D Worksheets — Grade 7 Make predictions and determine solutions using theoretical

Luna is helping her family plant a peach orchard in the Rio Grande Valley. They want to plant a total of 240 peach trees. If they plant 1/4 of the trees this month and plan to plant twice as many next month, how many trees will they plant next month?

1. 120 ✓
2. 80
3. 60
4. 100

Why: First, we find out how many trees Luna's family plants this month by calculating 1/4 of 240, which is 240 * 1/4 = 60 trees. Next, they plan to plant twice that amount next month, so we calculate 2 * 60 = 120 trees. Therefore, they will plant 120 trees next month.

Victoria is organizing a garden at her school in Lufkin, Texas. She has a total of 30 plants, consisting of cacti and succulents. The number of cacti is twice the number of succulents. How many cacti does Victoria have?

1. 10
2. 15
3. 20 ✓
4. 25

Why: Let the number of succulents be x. Then, the number of cacti is 2x. The total number of plants is the sum of cacti and succulents, or x + 2x = 30. Simplifying gives 3x = 30, leading to x = 10. Therefore, the number of cacti is 2x = 2 * 10 = 20.

Andrew is organizing a basketball tournament at his school in Amarillo, Texas. He has 12 teams participating in the tournament. Each team plays against every other team exactly once. How many total games will be played in the tournament?

1. 66 ✓
2. 72
3. 78
4. 84

Why: To find the total number of games played in a round-robin tournament where each team plays every other team once, we can use the formula: Total games = n(n - 1) / 2, where n is the number of teams. Here, n = 12, so Total games = 12(12 - 1) / 2 = 12 * 11 / 2 = 132 / 2 = 66. Thus, the total games played is 66.

Carolina is organizing a bake sale at her school in Galveston, Texas. She plans to sell cookies and brownies. She has 48 cookies and 36 brownies. To package them, she wants to create boxes that each contain the same number of cookies and brownies. What is the greatest number of complete boxes she can make if each box must contain an equal number of cookies and an equal number of brownies?

1. 6
2. 12 ✓
3. 8
4. 10

Why: To find the greatest number of complete boxes Carolina can make, we need to determine the greatest common divisor (GCD) of the number of cookies (48) and the number of brownies (36). The GCD of 48 and 36 is 12. This means Carolina can make 12 complete boxes, with each box containing 4 cookies (48 / 12 = 4) and 3 brownies (36 / 12 = 3). Therefore, the correct answer is 12.

Maxwell is studying the wildlife of Texas for his science project. He found that in a certain area, 15 out of 40 deer observed were male white-tailed deer. Additionally, he noted that there are 10 female deer also observed in that same area. What is the theoretical probability that a randomly selected deer from this area is either a male white-tailed deer or a female deer?

1. 3/8
2. 1/2
3. 5/8 ✓
4. 7/8

Why: To find the theoretical probability of selecting either a male white-tailed deer or a female deer, we first determine the total number of deer observed. There are 40 deer in total. We have 15 male white-tailed deer and 10 female deer, which totals 25 deer (15 males + 10 females). The probability is then calculated as the number of favorable outcomes (25) divided by the total outcomes (40): P(male or female) = 25 / 40 = 5/8.

In a survey conducted at a school in Amarillo, Texas, 60 students were asked about their favorite fruits. Out of those students, 25 said they like oranges, 30 said they like peaches, and 10 students said they like both oranges and peaches. What is the probability that a randomly selected student from the survey likes either oranges or peaches?

1. 0.75 ✓
2. 0.5
3. 0.33
4. 0.25

Why: To find the probability that a randomly selected student likes either oranges or peaches, we use the formula P(A or B) = P(A) + P(B) - P(A and B). First, we determine the number of students who like either fruit: 25 (oranges) + 30 (peaches) - 10 (both) = 45 students. Now, we find the probability: P(either) = 45 / 60 = 0.75. Therefore, the correct answer is 0.75.

Daniel is planning a trip to Enchanted Rock with his friends. They estimate that there will be a 40% chance of rain on the day of their visit. If they go on a day when there is a 60% chance that at least one of them will want to hike, what is the probability that it will rain and at least one of them will want to hike on that day? (Assume the events are independent.)

1. 0.24 ✓
2. 0.40
3. 0.60
4. 0.76

Why: To find the probability of both events happening, multiply the probability of rain (0.40) by the probability that at least one friend wants to hike (0.60). The calculation is 0.40 * 0.60 = 0.24. Therefore, the probability that it will rain and at least one of them will want to hike is 0.24.

Emma and her friends are planning a trip to Galveston Bay. They want to spend the entire day, and they estimate a 60% chance it will be sunny, a 25% chance it will be cloudy, and a 15% chance it will rain. If they decide to go only if it is either sunny or cloudy, what is the probability that they will go to Galveston Bay?

1. 0.85 ✓
2. 0.60
3. 0.75
4. 0.40

Why: To find the probability that Emma and her friends will go to Galveston Bay, we need to add the probabilities of it being sunny and cloudy. The probability of sunny is 60% (or 0.60) and the probability of cloudy is 25% (or 0.25). We add these two values: 0.60 + 0.25 = 0.85. Therefore, the probability that they will go to Galveston Bay is 0.85.