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Math Exercises: Inequality Word Problems





1. Find the greatest integer that is the solution of an inequality 1.6 - (3.2 - 0.2y) < 5.1 .


2. From the point A on the river bank tourists set sail on a motor boat downriver. The flow rate of the river is 2 km/h and the boat has its own speed of 18 km/h. To what distance from the point A can tourists swim so as the cruise would last no longer than 3 hours ?


3. Find such a natural number about which we can say: If we subtract 2 from this number and the result will be divided by three, we get a fraction that is less than number 1. What is the number ?


4. Find two-digit positive number less than 64 when its tens digit is less by 3 than units digit.


5. Tom got F at the beginning of the school year. How many times must he now get A in order to have B on the certificates ?


6. Find all two-digit numbers greater than 40, while less than 80, whose units digit is 4 less than the tens digit.


7. If a tourist will increase his speed by 1 km/h then in 4 hours he travels a distance greater than 20 km. If he reduce his speed by 1 km/h, in 5 hours he travels a distance of less than 20 km. What is the speed of the tourist ?


8. In the unknown two-digit number is its units digit less by one than its tens digit. If we add 7 to this number, the new number will be greater than 19, while less than 51. Find all two-digit numbers with those characteristics.


9. Find the fraction about which we can say: If the denominator is reduced by one, fraction equals to ½. By increasing the numerator by 20 we get the fraction which is greater than 2 while less than 3.


10. If a tractor driver plowed daily two more hectares than he planned, he would plow in 9 days more than 84 ha. If he plowed daily one hectare less than he planned, he would plow in 12 days not more than 84 ha. How many hectares would the tractor driver plow daily according to the plan ?


11. One leg of the right-angled triangle is 2 cm longer than the other leg. How long should be the first leg, if the hypotenuse must be longer than 10 cm ?


12. What values can m have, if the roots of the equation m2x2 + 2mx + 1 = 0 should have values in the range <3;5> ?


13. There are 8 liters of 26% solution in the vessel. How many percent must be the solution in the 10 liter vessel in order to the mix of both solutions is at least 50% and at most 60% solution ?







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