Cristina Mocanu Math Department

John scored 57 on his first test. What must least score on the second test if his average on both tests to be more than 67? (Scores of the exams are whole numbers.) Cristina Mocanu Math Department

Solution: Recall: The average of two numbers a and b is (a + b)/2 Let be x the score on the second test. Using the formula of the average and the given, (57 + x)/2 > x > 67 · 2 multiplying both sides by x > 134 x > 77 subtracting 57 from both sides Hence, John must score at least 78 on the second exam. Cristina Mocanu Math Department

The cost of the dress in the store is $50 more than the cost of a pair of shoes. Sarah plans to buy both items and has only $200. What is the greatest amount that Sarah can spend on the shoes? Cristina Mocanu Math Department

Solution: Let be x the cost of the shoes. Then the cost of the dress is x Both items cost: x + (x + 50) that must be less than 200. x + (x + 50) ≤ 200 x + x + 50 ≤ 200 combining like terms 2x ≤ 200 – 50 subtracting 50 in both sides 2x ≤ 150 x ≤ 150/2 dividing both sides by 2 x ≤ 75 Hence, the price of the shoes should not exceed $75. Cristina Mocanu Math Department