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01 Jan 2018, 10:22
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In each of the first two months of the year Janet saved $60 for her spring break trip. In the next three months she saved $75, $115, and $70 for the trip. How much does she need to save in the sixth and final month if she is to achieve her goal of $85 a month saved on average (arithmetic mean)?
A. $190
B. $130
C. $115
D. $110
E. $100
A. $190
B. $130
C. $115
D. $110
E. $100
01 Jan 2018, 14:29
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(60 + 60 + 75 + 115 + 70 + x) / 6 = 85
Solving for x:
380 + x = 510
x = $130 (Answer B)
Solving for x:
380 + x = 510
x = $130 (Answer B)
RusskiyLev
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14 Dec 2019, 05:18
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Quote:
In each of the first two months of the year Janet saved $60 for her spring break trip. In the next three months she saved $75, $115, and $70 for the trip. How much does she need to save in the sixth and final month if she is to achieve her goal of $85 a month saved on average (arithmetic mean)?
A. $190
B. $130
C. $115
D. $110
E. $100
A. $190
B. $130
C. $115
D. $110
E. $100
Initially, I thought that there are 7 months in total, but then analyzing the answer choices, I realized that the sixth month is the final one. Let us write down what we have:
January - $60
February - $60
March - $75
April - $115
May - $70
The money Janet needs to save for the last month (June) has to be equal to the amount which will give us $85 as an arithmetic average for 6 months.
The formula for arithmetic mean is the following: \(A = \frac{a_1 + a_2 ... + a_n }{ n}\)
We have \(A = \frac{(60 + 60 + 75 + 115 + 70 + x) }{ 6} = 85\)
\(A = \frac{(380 + x) }{ 6} = 85 \)
Therefore, \(380 + x = 85 * 6 = 510\)
\(x = 510 - 380 = 130\)
Answer: B
