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Word problems leading to inequalities
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 gt 67 57 + x gt 67 2 multiplying both sides by
2 57 + x gt 134 x gt 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 + 50 Both items cost x + (x + 50) that must be less
than 200 x + (x + 50) le 200x + x + 50 le 200 combining like terms2x le 200 ndash 50 subtracting 50 in both sides2x le 150 x le 1502 dividing both sides by 2x le 75 Hence the price of the shoes should not exceed
$75Cristina 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 gt 67 57 + x gt 67 2 multiplying both sides by
2 57 + x gt 134 x gt 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 + 50 Both items cost x + (x + 50) that must be less
than 200 x + (x + 50) le 200x + x + 50 le 200 combining like terms2x le 200 ndash 50 subtracting 50 in both sides2x le 150 x le 1502 dividing both sides by 2x le 75 Hence the price of the shoes should not exceed
$75Cristina 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 gt 67 57 + x gt 67 2 multiplying both sides by
2 57 + x gt 134 x gt 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 + 50 Both items cost x + (x + 50) that must be less
than 200 x + (x + 50) le 200x + x + 50 le 200 combining like terms2x le 200 ndash 50 subtracting 50 in both sides2x le 150 x le 1502 dividing both sides by 2x le 75 Hence the price of the shoes should not exceed
$75Cristina 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 + 50 Both items cost x + (x + 50) that must be less
than 200 x + (x + 50) le 200x + x + 50 le 200 combining like terms2x le 200 ndash 50 subtracting 50 in both sides2x le 150 x le 1502 dividing both sides by 2x le 75 Hence the price of the shoes should not exceed
$75Cristina Mocanu Math Department
Solution Let be x the cost of the shoes Then the cost of
the dress is x + 50 Both items cost x + (x + 50) that must be less
than 200 x + (x + 50) le 200x + x + 50 le 200 combining like terms2x le 200 ndash 50 subtracting 50 in both sides2x le 150 x le 1502 dividing both sides by 2x le 75 Hence the price of the shoes should not exceed
$75Cristina Mocanu Math Department
