Scott earned 20 points more on his most recent math test than he earned on the previous test. If he earned at least 80 points on the most recent math test, how many points did he earn on the previous test?
A. $s \leq 60$
B. $s \geq 60$
C. $s<60$
D. $s>60$
Answer (1)
Let s represent the points Scott earned on the previous test.
Express the score on the most recent test as s + 20 .
Formulate the inequality s + 20 ≥ 80 .
Solve the inequality to find s ≥ 60 , meaning Scott earned at least 60 points on the previous test. s ≥ 60
Explanation
Setting up the inequality Let s be the number of points Scott earned on the previous test. We know that Scott earned 20 points more on his most recent math test than he earned on the previous test. So, the score on his most recent test is s + 20 . We also know that he earned at least 80 points on the most recent math test, which means s + 20 is greater than or equal to 80. This can be written as an inequality: s + 20 ≥ 80
Solving the inequality To find the possible values of s , we need to solve the inequality s + 20 ≥ 80 . We can do this by subtracting 20 from both sides of the inequality: s + 20 − 20 ≥ 80 − 20 s ≥ 60 This means that Scott earned at least 60 points on the previous test.
Final Answer Therefore, the number of points Scott earned on the previous test is greater than or equal to 60.
Examples
Understanding inequalities is crucial in many real-life situations. For instance, imagine you're saving money for a new bicycle that costs at least $200. If you've already saved 120 , yo u c an u se anin e q u a l i t y t o d e t er min e h o w m u c hm oreyo u n ee d t os a v e . L e t x$ be the additional amount you need to save. The inequality would be 120 + x ≥ 200 . Solving for x , you find that x ≥ 80 , meaning you need to save at least $80 more to afford the bicycle. This concept applies to budgeting, time management, and many other areas where you need to meet certain minimum or maximum requirements.
