1. Roger is a wildlife researcher who has been hired to study and track the population of bears in a national park. In year 1 of the study, Roger determines that the park is home to X bears. In year 2, the population has increased to X+10 bears, and in year 3, the population has increased to 2(x+10) bears.

Question

1. Roger is a wildlife researcher who has been hired to study and track the population of bears in a national park. In year 1 of the study, Roger determines that the park is home to X bears. In year 2, the population has increased to X+10 bears, and in year 3, the population has increased to 2(x+10) bears.

a. Use the distributive property to rewrite the bear population in year 3 without needing to use parentheses.
b. The total number of bears in the park during year 2 is 42. Write and solve a linear equation to determine how many bears were in the park during year 1.
c. The total number of bears in the park during year 3 is 50. Write and solve a linear equation to determine how many bears were in the park during year 1. Note that this answer will not be the same as the answer you got in part b.
d. During year 4, bad weather keeps Roger from finding the exact number of bears in the park. However, he knows that y+5>38, where y is the number of bears in the park year 4. Solve the inequality, and give three possible values for Y.
2. Jen is a wildlife researcher higher, the population of wolves in the same national park. In year 1 of the study, there are z wolves; in year 2 of the study, there are 7+z wolves; and in year 3 of the study, there are 3z-3 . The number of wolves in year 2 is equal to the number of wolves in year 3.
a. And solve a linear equation to determine the value of Z.
b. Jin rates and expiration to describe the number of wolves in year 4 of the study. The expression is (x+a)(x-b), where an and b are whole numbers greater than 1 and less than 10. Write an expression that could be the expression Jin uses to describe the number of wolves in the park during year 4 of the study. Then multiply the two terms of the expression.

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1 answer
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Answer 1

Bot GPT 3.5 answered
8 months ago

a. 2(x + 10) = 2x + 2(10) = 2x + 20

b. Let the number of bears in year 1 be represented by the variable y. We are given that in year 2, the population is 42 bears, so we can set up the equation:

y + 10 = 42
y = 42 - 10
y = 32

Therefore, in year 1 there were 32 bears in the park.

c. Let y represent the number of bears in year 1. We are given that in year 3, the population is 50 bears, so we can set up the equation:

2(y+10) = 50
2y + 20 = 50
2y = 50 - 20
2y = 30
y = 15

Therefore, in year 1 there were 15 bears in the park.

d. Solve the inequality y + 5 > 38:
y > 33

Three possible values for y could be 34, 35, or 36.

2.
a. Set up the equation since the number of wolves in year 2 is equal to the number of wolves in year 3:

7 + z = 3z - 3
7 + 3 = 3z - z
10 = 2z
z = 5

Therefore, in year 1 there were 5 wolves in the park.

b. An expression that could describe the number of wolves in year 4 could be (z + a)(z - b), where a and b are whole numbers greater than 1 and less than 10. One example expression could be (5 + 4)(5 - 2) which simplifies to (9)(3) = 27.