Inequality Word Problems 2
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Question 1 of 5
1. Question
Michael wants to buy a new 4K HD TV. The cheapest TV is advertised as `$1100`. He has saved `$300` already and has a part-time job earning `$160` per week. How many weeks will it take before he has saved up enough to buy the cheapest TV?Hint
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Identify the known values
`\text(Price of TV)= $1100``\text(Michael’s savings)= $300``\text(Earnings per week)= $160``\text(Number of weeks)= n`First, form an inequality from the problemSince Michael needs to save up at least `$1100` to buy the TV, he must keep earning `$160` per week until he has greater than or equal to `$1100`.Hence, the inequality can be written as:`300+160n` `≥` `1100` Next, make sure that only `n` is on the left side`300+160n` `≥` `1100` `300+160n` `-300` `≥` `1100` `-300` Subtract `300` from both sides `160n` `divide160` `≥` `800` `divide160` Divide both sides by `160` `n` `≥` `5` `n≥5` -
Question 2 of 5
2. Question
A hard drive holds about `75` hours of movie videos. So far it has `52` hours. You estimate that each movie is `2` hours long. How many movies can we transfer on top of the movies that are already in the hard drive?Hint
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Identify the known values
`\text(Size of hard drive)= 75``\text(Hours already on hard drive)= 52``\text(Number of hours per movie)= 2``\text(Number of movies)= n`First, form an inequality from the problemSince the hard drive only has a capacity of `75` hours, the total number of `2` hour movies to be added on top of the `52` hours worth that is already on the hard drive must be less than or equal to `75`.Hence, the inequality can be written as:`52+2n` `≤` `75` Next, make sure that only `n` is on the left side`52+2n` `≤` `75` `52+2n` `-52` `≤` `75` `-52` Subtract `52` from both sides `2n` `divide2` `≤` `23` `divide2` Divide both sides by `2` `n` `≤` `11.5` Since we can only add a whole movie and we cannot go over `75`, we need to round down the answer to `n≤11``n≤11` -
Question 3 of 5
3. Question
James currently weighs `108` kg. He wants to weigh less than `90` kg. If he can lose an average of `1 1/2` kg per week through exercise and diet, how long will it take to reach his goal?Hint
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Identify the known values
`\text(Jame’s current weight)= 108 kg``\text(Jame’s goal)= 90 kg``\text(Weight lost per week)= 1 1/2 kg``\text(Number of weeks)= n`First, form an inequality from the problemSince James wants to weigh less than `90` kg, he must keep losing `1 1/2` every week until he weighs less than `90` kg.Hence, the inequality can be written as:`108-1 1/2n` `<` `90` Next, make sure that only `n` is on the left side`108-1 1/2n` `<` `90` `108-1 1/2n` `-108` `<` `90` `-108` Subtract `108` from both sides `-1 1/2n` `divide(-1 1/2)` `<` `-18` `divide(-1 1/2)` Divide both sides by `-1 1/2` `n` `>` `12` Flip the inequality `n``>``12` -
Question 4 of 5
4. Question
A medium-sized bag of potatoes weighs `1 ` kg more than a small bag. A large bag weighs `4` kg more than a small bag. If the total weight is at most `14` kg, what is the most that a small bag could weigh?Hint
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Identify the known values
`\text(Total weight of bags) =` maximum of `14``\text(Small-sized bag(S))= s``\text(Medium-sized bag(M))= s+1``\text(Large-sized bag(L))= s+4`First, form an inequality from the problemThe total weight of the three bags must be less than or equal to `14` kg.Hence, the inequality can be written as:`S+M+L` `≤` `14` Next, make sure that only `n` is on the left side`S``+``M``+``L` `≤` `14` `s``+``s+1``+``s+4` `≤` `14` Substitute the known values `3s+5` `≤` `14` Combine like terms `3s+5` `-5` `≤` `14` `-5` Subtract `5` from both sides `3s` `divide3` `≤` `9` `divide3` Divide both sides by `3` `s` `≤` `3` `s≤3` -
Question 5 of 5
5. Question
Jack is flying an air balloon at an altitude of `16000` feet and is experiencing some bad weather. For him to fly safely, Jack needs to increase his altitude to at least `17000` feet or decrease his altitude to no more than `13000` feet. Form an inequality.The number lines below are scaled as `1:1000`ftHint
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A compound inequality consists of two inequalities joined together by AND or OR.First, form an inequality from the problemThe height of the balloon must be at least `17000` feet `h` `≥` `17000` The height of the balloon must be no more than `13000` feet `h` `≤` `13000` `h≥17000` OR `h≤13000`The first given inequality has a greater than or equal to (`≥`) sign.Hence, place a solid circle above `17000` and attach an arrow pointing to the right to represent all values greater than `17000`.
The second given inequality has a less than or equal to (`≤`) sign.Hence, place a solid circle above `13000` and attach an arrow pointing to the left to represent all values less than `13000`.
Finally, combine the two number lines.