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06 May 2022, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
67% (03:16) correct
33%
(03:17)
wrong
based on 227
sessions
History
Date
Time
Result
Not Attempted Yet
3 men and 4 boys can earn $756 in 7 days. 11 men and 13 boys can earn $3008 in 8 days. In what time will 7 men with 9 boys earn $2480?
A. 8 days
B. 10 days
C. 12 days
D. 15 days
E. 20 days
Are You Up For the Challenge: 700 Level Questions
A. 8 days
B. 10 days
C. 12 days
D. 15 days
E. 20 days
Are You Up For the Challenge: 700 Level Questions
06 May 2022, 03:49
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We are given \(3m + 4b = 756\) in 7 days (1), and \(11m + 13b = 3008\) in 8 days (2), and want to solve for the time it will take 7 men with 9 boys to make 2480.
The best strategy here is to make everything in terms of earnings for a single day worked, solve for how much 7 men and 9 boys make in a single day and use that to divide 2480 to see how many days it will take.
(1) \(3m + 4b = 756\) in 7 days. Which means that each day they earn \(\frac{756}{7}=108\)
(2) \(11m + 13b = 3008\) in 8 days. Which means that each day they earn \(\frac{3008}{8} = 376\)
Multiplying \(3m + 4b = 108\) through by 2 gives: \(6m + 8b = 216\) (we are missing an extra m+b still)
Subtracting \(6m + 8b = 216\) from \(11m + 13b = 376\) gives: \(5m + 5b = 160\), dividing through by 5 will make it: \(m + b = 32\).
Adding \(m + b = 32\) to \(6m + 8b = 216\) gives: \(7m + 9b = 248\)
Therefore, for 7 men and 9 boys to make 2480, it will take them \(\frac{2480}{248} = 10\) days
Answer B.
The best strategy here is to make everything in terms of earnings for a single day worked, solve for how much 7 men and 9 boys make in a single day and use that to divide 2480 to see how many days it will take.
(1) \(3m + 4b = 756\) in 7 days. Which means that each day they earn \(\frac{756}{7}=108\)
(2) \(11m + 13b = 3008\) in 8 days. Which means that each day they earn \(\frac{3008}{8} = 376\)
Multiplying \(3m + 4b = 108\) through by 2 gives: \(6m + 8b = 216\) (we are missing an extra m+b still)
Subtracting \(6m + 8b = 216\) from \(11m + 13b = 376\) gives: \(5m + 5b = 160\), dividing through by 5 will make it: \(m + b = 32\).
Adding \(m + b = 32\) to \(6m + 8b = 216\) gives: \(7m + 9b = 248\)
Therefore, for 7 men and 9 boys to make 2480, it will take them \(\frac{2480}{248} = 10\) days
Answer B.
General Discussion
06 May 2022, 07:47
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Ans:B
3m+4b=108
11m+13b=376
solving= m=20,b=12
2430=(7*20+9*12)*days
days=10
3m+4b=108
11m+13b=376
solving= m=20,b=12
2430=(7*20+9*12)*days
days=10
