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June 2017 p62 q1
2427
Rani and Diksha go shopping for clothes.
(i) Rani buys 4 identical vests, 3 identical sweaters and 1 coat. Each vest costs $5.50 and the coat costs $90. The mean cost of Rani’s 8 items is $29. Find the cost of a sweater.
(ii) Diksha buys 1 hat and 4 identical shirts. The mean cost of Diksha’s 5 items is $26 and the standard deviation is $0. Explain how you can tell that Diksha spends $104 on shirts.
Solution
(i) Let the cost of a sweater be \(x\).
The total cost of the items is given by:
\(4 \times 5.5 + 3x + 90 = 8 \times 29\)
\(22 + 3x + 90 = 232\)
\(112 + 3x = 232\)
\(3x = 120\)
\(x = 40\)
Thus, the cost of a sweater is $40.
(ii) Since the standard deviation is $0, all items cost the same. Therefore, the cost of each item is $26. Diksha buys 4 shirts, so the total cost for the shirts is: