Answer :
Alright, let's break down the problem step-by-step.
1. Identify the scores John already has: John already has scores of 72, 78, and 70.
2. Calculate the total of these scores:
[tex]\[ 72 + 78 + 70 = 220 \][/tex]
3. Determine the minimum total score required to pass the class: John needs at least 289 points to pass.
4. Find out how many more points John needs to achieve the required score:
[tex]\[ \text{Points needed} = 289 - 220 = 69 \][/tex]
5. Form the inequality to represent the situation: We need to establish an inequality that represents the scenario where John needs `x` more points to reach or exceed the required 289 points.
Thus, the inequality would be:
[tex]\[ 220 + x \geq 289 \][/tex]
Now, let’s look at the options provided:
A. [tex]\( 72 + 78 + 70 + x < 289 \)[/tex] – This is incorrect because this inequality tells John he needs less than 289 points in total, which does not align with the requirement of at least 289 points.
B. [tex]\( 72 + 78 + 70 + x > 289 \)[/tex] – This is incorrect because it suggests John needs more than 289 points, which is not a necessity; he needs at least 289.
C. [tex]\( 72 + 78 + 70 + x \leq 289 \)[/tex] – This incorrect because it suggests the total score could be less than or equal to 289, failing to meet or exceed the requirement of at least 289 points.
D. [tex]\( 72 + 78 + 70 + x \geq 289 \)[/tex] – This is the correct inequality because it properly represents that John’s current scores plus the additional points he needs must be at least 289.
Therefore, the best answer is:
D. [tex]\( 72 + 78 + 70 + x \geq 289 \)[/tex]
1. Identify the scores John already has: John already has scores of 72, 78, and 70.
2. Calculate the total of these scores:
[tex]\[ 72 + 78 + 70 = 220 \][/tex]
3. Determine the minimum total score required to pass the class: John needs at least 289 points to pass.
4. Find out how many more points John needs to achieve the required score:
[tex]\[ \text{Points needed} = 289 - 220 = 69 \][/tex]
5. Form the inequality to represent the situation: We need to establish an inequality that represents the scenario where John needs `x` more points to reach or exceed the required 289 points.
Thus, the inequality would be:
[tex]\[ 220 + x \geq 289 \][/tex]
Now, let’s look at the options provided:
A. [tex]\( 72 + 78 + 70 + x < 289 \)[/tex] – This is incorrect because this inequality tells John he needs less than 289 points in total, which does not align with the requirement of at least 289 points.
B. [tex]\( 72 + 78 + 70 + x > 289 \)[/tex] – This is incorrect because it suggests John needs more than 289 points, which is not a necessity; he needs at least 289.
C. [tex]\( 72 + 78 + 70 + x \leq 289 \)[/tex] – This incorrect because it suggests the total score could be less than or equal to 289, failing to meet or exceed the requirement of at least 289 points.
D. [tex]\( 72 + 78 + 70 + x \geq 289 \)[/tex] – This is the correct inequality because it properly represents that John’s current scores plus the additional points he needs must be at least 289.
Therefore, the best answer is:
D. [tex]\( 72 + 78 + 70 + x \geq 289 \)[/tex]
