Question

Rodney is helping to make hamburgers for the football game. He's made 10 hamburgers so far. His coach asked him to make at least 30 hamburgers but no more than 80. Solve the inequality and interpret the solution.

30 ≤ x + 10 ≤ 80

20 ≥ x ≥ 70; Rodney needs to make less than 20 more hamburgers or more than 70.
40 ≤ x ≤ 90; Rodney needs to make at least 40 more hamburgers but no more than 90.
40 ≥ x ≥ 90; Rodney needs to make less than 40 more hamburgers or more than 90.
20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70.

Answer 1

20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70

Explanation:

Let

x ----> the numbers of hamburgers that Rodney needs to make

we know that

`x+10\geq 30` ----> inequality A

`x+10\leq 80` -----> inequality B

Solve the inequality A

`x\geq 30-10`

`x\geq 20\ hamburgers`

Solve the inequality B

`x\leq 80-10`

`x\leq 70\ hamburgers`

so

The solution of the system of inequalities is the interval

[20,70]

`20 \leq x \leq 70`

All whole numbers greater than or equal to 20 hamburgers and less than or equal to 70 hamburgers

therefore

Rodney needs to make at least 20 more hamburgers but no more than 70.

Answer 2

Option D (20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70).

Explanation:

The given inequality is 30 ≤ x + 10 ≤ 80 . There are basically two inequalities. One is 30 ≤ x + 10 and x + 10 ≤ 80. x is the number of hamburgers that are to be made, 10 is the number of hamburgers already made, 30 is the lower limit of the hamburgers required, and 80 is the upper limit of the hamburgers required. The question requires to solve the inequality. To solve this, the inequality will be separated as done above.

1)

30 ≤ x + 10.

20 ≤ x.

2)

x + 10 ≤ 80.

x ≤ 70.

Now combining the two inequality gives:

20 ≤ x ≤ 70. So Rodney needs to make at least 20 more hamburgers but no more than 70. Therefore, Option D is the correct answer!!!