Colin weighs himself at 93 kg to the nearest kg. Write, a) The upper bound of his weight, b) The lower bound of his weight, c) An inequality to show the range of values the weight... Colin weighs himself at 93 kg to the nearest kg. Write, a) The upper bound of his weight, b) The lower bound of his weight, c) An inequality to show the range of values the weight could have.
Understand the Problem
The question asks for the upper and lower bounds of Colin's weight based on the fact that he weighs 93 kg to the nearest kg. It also requires writing an inequality showing the range of values that his weight could take.
Answer
a) $93.5 \, \text{kg}$, b) $92.5 \, \text{kg}$, c) $92.5 < \text{Weight} < 93.5$
Answer for screen readers
a) The upper bound of his weight: $93.5 , \text{kg}$
b) The lower bound of his weight: $92.5 , \text{kg}$
c) The inequality showing the range of values: $92.5 < \text{Weight} < 93.5$
Steps to Solve
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Understanding Upper Bound The upper bound is what Colin's weight could reach without exceeding the rounded weight of 93 kg. Since he weighs to the nearest kg, the maximum weight can be calculated by adding 0.5 kg to 93 kg.
$$ \text{Upper Bound} = 93 + 0.5 = 93.5 , \text{kg} $$
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Understanding Lower Bound The lower bound is what Colin's weight could drop to without being less than the rounded weight of 93 kg. To find this, subtract 0.5 kg from 93 kg.
$$ \text{Lower Bound} = 93 - 0.5 = 92.5 , \text{kg} $$
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Writing the Inequality To express the range of possible weight values, combine the upper and lower bounds into an inequality. Colin's actual weight can range from the lower bound to the upper bound.
$$ 92.5 < \text{Weight} < 93.5 $$
a) The upper bound of his weight: $93.5 , \text{kg}$
b) The lower bound of his weight: $92.5 , \text{kg}$
c) The inequality showing the range of values: $92.5 < \text{Weight} < 93.5$
More Information
Colin's weight could be any value between 92.5 kg and 93.5 kg. This method involves understanding how rounding works in measurements and using simple arithmetic to establish bounds.
Tips
- Confusing upper and lower bounds; remember that the upper bound includes adding 0.5 kg, while the lower bound involves subtracting 0.5 kg.
- Not expressing the inequality correctly or leaving out the strict inequalities.
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