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Answer :
Answer:
a) 40kg b) 245g
Step-by-step explanation:
a) the total mass of the group of 4 students is 30 x 4 = 120
the total mass of the group of 5 students is 32 x 5 = 160
160 - 120 = 40
b) the total mass of 5 articles is 215 x 5 = 1075
the total mass of 6 articles is 220 x 6 = 1320
1320 - 1075 = 245
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Final answer:
The mass of the student who joined the group is 40 kg, and the mass of the sixth article added is 245 g. These calculations were made using the definition of mean and the known total masses before and after the new additions.
Explanation:
To solve part (a), we apply the concept of mean of a set of numbers. The mean mass of the original group of four students is 30 kg. The total mass of these students can be calculated by multiplying the mean by the number of students, which results in 4 students × 30 kg/student = 120 kg. When a fifth student joins the group, the mean mass becomes 32 kg, indicating that the total mass of all students is 5 students × 32 kg/student = 160 kg. To find the mass of the student who joined the group, subtract the original group's total mass from the new total mass:
Mass of the fifth student = 160 kg - 120 kg = 40 kg.
For part (b), we use the same approach. The mean mass of five articles is 215 g, giving us a total mass of 5 articles × 215 g/article = 1075 g. When a sixth article is added, the mean increases to 220 g, hence the total mass becomes 6 articles × 220 g/article = 1320 g. To determine the mass of the sixth article, subtract the previous total mass from the new total mass:
Mass of the sixth article = 1320 g - 1075 g = 245 g.
