A family is going on vacation and they are packing their bags for their flight. They have packed four bags which weigh (in kg) 16, 17, 21, and 26. They need to pack one more bag. Write an inequality to represent the weights the next bag could have so that the average (mean) is lower than 22. Use x to represent the weight of the next bag. Simplify your answer as much as possible.
Question
A family is going on vacation and they are packing their bags for their flight. They have packed four bags which weigh (in kg) 16, 17, 21, and 26. They need to pack one more bag. Write an inequality to represent the weights the next bag could have so that the average (mean) is lower than 22. Use x to represent the weight of the next bag. Simplify your answer as much as possible.
Solution
To find the average weight of the bags, you add up the weights of all the bags and divide by the number of bags. The family has already packed four bags and they want to pack one more, so the total number of bags will be 5.
The weights of the four bags they have already packed are 16 kg, 17 kg, 21 kg, and 26 kg. So, the total weight of these four bags is 16 + 17 + 21 + 26 = 80 kg.
They want the average weight of all five bags to be less than 22 kg. So, the total weight of all five bags should be less than 22 * 5 = 110 kg.
Let's use x to represent the weight of the fifth bag. The inequality that represents the weights the fifth bag could have so that the average is lower than 22 is:
80 + x < 110
To simplify this inequality, subtract 80 from both sides:
x < 110 - 80
So, the simplified inequality is:
x < 30
This means the fifth bag must weigh less than 30 kg for the average weight of all five bags to be less than 22 kg.
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