t&w q8

[Saumyojit]

A, b and c working together completed a job in 10 days. However, c only worked for the first three days when 37/100 of the job was done. Also, the work done by a in 5 days is equal to the work done by b in 4 days. How many days would be required by the fastest worker to complete the entire work?

Wa per day * 5days = Wb per day * 7 days


(Wa + Wb + Wc ) * 3 days = 37/ 100


(Wa + Wb ) * 7 days =1 - 37/100


=> Wa * 5 days + Wb * 4 days + Wa *2 days + Wb * 3 days = 63/100

=> Wa * 5 days + Wa * 5 days + Wa *2 days + Wb * 3 days = 63/100

=> 12 Wa + 3Wb = 63/100

Work by A in 5 days = x
per day Work by A = x/5

Work by B in 4 days = x
per day Work by B = x/4


Work by A in 3 days = 3x / 5

Work by B in 3 days = 3x / 4




3x / 5 + 3x / 4 + ( Work per day by C * 3 days )= 37/ 100 . another equation

 

[Dr.Peterson]

A, b and c working together completed a job in 10 days. However, c only worked for the first three days when 37/100 of the job was done. Also, the work done by a in 5 days is equal to the work done by b in 4 days. How many days would be required by the fastest worker to complete the entire work?

Wa per day * 5days = Wb per day * 7 days
(Wa + Wb + Wc ) * 3 days = 37/ 100
(Wa + Wb ) * 7 days =1 - 37/100

Good work writing the equations; I'd simplify the variable names and leave out the units, making it

5a = 7b​

3(a+b+c) = 37/100​

7(a+b) = 63/100​

=> Wa * 5 days + Wb * 4 days + Wa *2 days + Wb * 3 days = 63/100

=> Wa * 5 days + Wa * 5 days + Wa *2 days + Wb * 3 days = 63/100

=> 12 Wa + 3Wb = 63/100

This accomplishes nothing, as it has not eliminated a variable.

I'd just start solving the system of equations by eliminating one variable at a time. I'm inclined to clear fractions and make the equations

5a = 7b​

300a+300b+300c = 37​

700a+700b = 63​

Now you might eliminate a using the first equation (you'll see why I chose a rather than b once you do it); or combine the first and thied equation to eliminate whichever variable you like.

How much have you learned about solving systems of linear equations? This should not be hard, and doesn't require the sort of non-standard strategies you are trying. Certainly bringing in a new variable only complicates things!