Confusing simultaneous linear equation

Question

a) 2 boys and 5 girls can finish a piece of work in 4 days . 4 boys and 4 girls can finish the same work in 3 days. If a girl is paid

$750 every day, what would be the total expenditure to complete the work?

Ans: $2700

 

b) 8 men and 12 women can finish a piece of work in 10 days, 6 men and 8 women can finish the same work in 14 days. how many days does each (1 man and 1 woman separately) need to complete the work?

Ans: 140days , 240 days

Answer 1

Part a) THE PAY RATE IS $75 NOT $750!!!

b stands for boy and g stands for g, set the following system of equations:

2b+5g=1/4

4b+4g=1/3

solving this gives you g=1/36. What does it mean? it means if a girl works by herself she will finish this work in 36 days. With the rate of 75 per day, she gets 75*36=$2700 to finish this job

 

Part b) Similarly for this part m and w stand for men and women respectively. Set the following system of equations:

8m+12w=1/10

6m+8w=1/14

 

solving this gives m=1/140, and w=1/280, which means a man can finish 1/140 pieces of the work a day, and it takes 140 days to him to finish the whole work. Similarly it takes 280 for a woman to finish this job (there is a typo in your answer 240 is not correct)

 

I hope it helps. Let me know if you need more explanations.

Answer 2

It is confusing because we do not know how much the boys are paid per day.

Nor do we have an equation to find it.

Also, double check the numbers in BOTH of the problems. I got a negative answer for the

boys' work rate.