Our everyday lives are filled with models and applications of mathematics. Come up with a system of two equations and two variables. Provide a solution to the problem.

Jack and Lisa does total of 10 hours of work per day. At the same time jack earns 10 $ per hour and Lisa earns 15 $ per hour. If combined earning of jack and lisa is 125 $. How many hours of work they separately did?

Solution:

Lets say no. of hours Jack worked = x

and no. of hours Lisa worked = y

Now according to question, total no of hours both worked

=10 = x+y

=> x+y = 10 ---------(i)

Also total earning of both jack and lisa = 125$ = 10x +15 y

=> 10x+15y = 125

=>2x+3y = 25 -----(ii)

Thus system of equations is:

x+y = 10

2x+3y = 25

Inserting equation multiplying equation (i) by 2 and subtracting it from (ii) we get=>

3y - 2y = 30-25

=> y = 5

and x = 10-y = 10-5 = 5 hours

Hence both x and y works 5 hours each

Apr 23rd, 2015

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