Inequality Word Problems 1
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Question 1 of 5
1. Question
The base of a triangle is bigger than its height. Find the possible values of `x`.
Hint
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`\text(Base)= 11+x``\text(Height)= 15`First, form an inequality from the problemThe base of the triangle is bigger than its height `11+x` `>` `15` Next, make sure that only `x` is on the left side`11+x` `>` `15` `11+x` `-11` `>` `15` `-11` Subtract `11` from both sides `x` `>` `4` Evaluate Check our workTo confirm that `4` is less than `x`, substitute `x=5` to the original inequality`11+x` `>` `15` `11+``5` `>` `15` Substitute `x=5` `16` `>` `15` Since the inequality is true, the representation is correct`x``>``4` -
Question 2 of 5
2. Question
Donald has saved `$700` for one-on-one tennis coaching. A coach recommends `20` hours of coaching. Write an inequality for the possible hourly rate that Donald could afford to pay for the coaching.Hint
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`\text(Donald’s savings)= $700``\text(Recommended hours of training)= 20``\text(Rate per hour)= r`First, form an inequality from the problemSince we know that Donald can only pay a maximum of `$700` for `20` hours of training, the amount he can pay hourly can only be less than or equal to a certain amount.Hence, the inequality can be written as:`700/r` `≤` `20/1` Next, make sure that only `r` is on the left side`700/r` `≤` `20/1` `20r` `≤` `700` Cross multiply `20r``divide20` `≤` `700``divide20` Divide both sides by `20` `r` `≤` `35` `r≤35` -
Question 3 of 5
3. Question
The perimeter of this triangle must be no more than 75.8 cm. Find an expression that represents all possible `x` values.
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The perimeter of a triangle is the sum of all sides.First, form an inequality from the problemThe perimeter of the triangle must be no more than `75.8` `19.1+31.6+x` `≤` `75.8` Next, make sure that only `x` is on the left side`19.1+31.6+x` `≤` `75.8` `50.7` `+x` `≤` `75.8` Combine like terms `50.7+x` `-50.7` `≤` `75.8` `-50.7` Subtract `50.7` from both sides `x` `≤` `25.1` `x≤25.1` -
Question 4 of 5
4. Question
The total maximum weight of luggage on a first-class international flight is `50` kg per person. If Lucy has three suitcases and the first suitcase weighs `17` kg and the second weighs `15` kg, how much will the third bag weigh?Hint
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`\text(Maximum weight of luggage)= 50 kg``\text(Weight of first bag)= 17 kg``\text(Weight of second bag)= 15 kg``\text(Weight of third bag)= x`First, form an inequality from the problemSince the maximum weight of luggage Lucy can bring is `50` kg, the total weight of all her bags must be less than or equal to `50` kg.Hence, the inequality can be written as:`17+15+x` `≤` `50` Next, make sure that only `x` is on the left side`17+15+x` `≤` `50` `32+x` `≤` `50` Combine like terms `32+x` `-32` `≤` `50` `-32` Subtract `32` from both sides `x` `≤` `18` `x≤18` -
Question 5 of 5
5. Question
Jane has `$85` to spend with her friends. They ordered `$33` worth of pizzas, `$11` worth of bread and `$17` on drinks. How much can Jane spend on desserts?Hint
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Identify the known values
`\text(Jane’s money)= $85``\text(Cost of pizza)= $33``\text(Cost of bread)= $11``\text(Cost of drinks)= $17``\text(Cost of dessert)= x`First, form an inequality from the problemSince Jane only have `$85` to spend, the total cost of the meal must be less than or equal to `$85`.Hence, the inequality can be written as:`33+11+17+x` `≤` `85` Next, make sure that only `x` is on the left side`33+11+17+x` `≤` `85` `61+x` `≤` `85` Combine like terms `61+x` `-61` `≤` `85` `-61` Subtract `61` from both sides `x` `≤` `24` `x≤24`
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