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Here's a problem from a 6th Grade textbook:

A project was carried out by a 3-man brigade working for 5 days and a 4-man brigade working for 4 days. $390 was paid for the whole project. How much was the first brigade paid if the productivity of all the workers is the same?

My attempt was to first calculate the whole effort needed for the project in $man*days$, which is $5*3 + 4*4 = 31man*days$. Then estimate how much one $man*day$ costs - $\frac {390} {31} dollars$. Therefore, the first brigade, which has made $15man*days$ effort, must receive $15* \frac {390} {31} dollars$. However, the "correct" answer in the answer key is $150 dollars$. I am almost sure that the answer key is wrong, but decided to ask just in case I'm missing something subtle or obvious.

P.S. I have no idea how to tag this question. Please suggest.

Armen Tsirunyan
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    Are you sure it wasn't the four man brigade working for six days (or six men for four days) - that would make sense. If not, I would suspect a typo in the text. – Mark Bennet Oct 24 '14 at 10:13
  • Mark Bennet gave one way to reconcile the numbers. Another way would be if the total paid for the job is $310. – paw88789 Oct 24 '14 at 10:34

2 Answers2

1

Since the productivity of all the workers is the same:

  • A $3$-man brigade working for $5$ days is equivalent to $1$ man working for $15$ days
  • A $4$-man brigade working for $4$ days is equivalent to $1$ man working for $16$ days

Since $390$ dollars were paid for the whole project:

  • The $1st$ brigade was paid $\frac{15}{15+16}\cdot390\approx188.7$ dollars
  • The $2nd$ brigade was paid $\frac{16}{15+16}\cdot390\approx201.3$ dollars
barak manos
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You could form an equation

If x stood for men and y for days, you could then write an equation.

$$3x+5y+4x+4y = 390$$

$$7x+9y =390--(i)$$

and use the fact that Productivity of 1st brigade equals 2nd brigade

$$3x+5y=4x+4y$$ $$3x-4x+5y-4y=0$$ $$-x+y=0--(ii)$$

You could use (i) and (ii) and solve further, but if you do so with these equations you would get negative reward for productivity which cannot be true. Therefore, there is something wrong with the question as it is pointed by the first comment.

Shoaibkhanz
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