MHB Solve Ratio Word Problem: Find Value of x

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The discussion revolves around solving a ratio word problem involving work done by two groups of men over different days. The first group consists of (x-3) men working for (2x+1) days, while the second group has (2x+1) men working for (x+4) days, with their work ratio given as 3:10. The equation derived from the problem is set up as the ratio of total work done by both groups, leading to the expression y(2x+1)(x-1) for the first group. A point of confusion arises regarding whether the numerator of the fraction should be y(2x+1)(x-1) or y(2x+1)(x-3). The goal is to determine the correct value of 'x' based on these calculations.
kuheli
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hi ,

this is one simple math but i am not getting the answer.

the work done by (x-3) men in (2x+1) days and the work done by (2x+1)men in (x+4) days are in the ratio of 3:10.find the value of 'x'.
 
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Re: ratio

kuheli said:
hi ,

this is one simple math but i am not getting the answer.

the work done by (x-3) men in (2x+1) days and the work done by (2x+1)men in (x+4) days are in the ratio of 3:10.find the value of 'x'.

suppose the amount of work done by a man per day is y

(x-3) men done y(x-3) per day, and y(x-3)(2x+1) per (2x+1) days
Total work done by the first group is y(x-1)(2x+1)
In same manner the other group will do y(2x+1)(x+4)
we have to solve this equation
\frac{y(2x+1)(x-1)}{y(2x+1)(x+4)} = \frac{3}{10}
 
Re: ratio

Amer said:
suppose the amount of work done by a man per day is y

(x-3) men done y(x-3) per day, and y(x-3)(2x+1) per (2x+1) days
Total work done by the first group is y(x-1)(2x+1)
In same manner the other group will do y(2x+1)(x+4)
we have to solve this equation
\frac{y(2x+1)(x-1)}{y(2x+1)(x+4)} = \frac{3}{10}

do you think the numerator of the fraction is
y(2x+1)(x-1) or y(2x+1)(x-3) ?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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