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Working his way through school, Joe works two part-time jobs for a total of 30 hours a week. Job A pays $5.90 per hour, and Job B pays $7.20 per hour. How many hours did he work at each job the week that he made $197.80? (Round to two decimal places if necessary.)

Answer :

Joe worked for 14 hours at Job A and for 16 hours at Job B.

What are simultaneous equation?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Now it is given that,

Joe works two part-time jobs for a total of 30 hours a week.

Let x be the number hours that Joe worked at job A in a week.

and y be the number hours that Joe worked at job B in a week.

⇒ x + y = 30 ...(i)

Now Job A pays $5.90 per hour,

Therefore,

Amount receive from Job A = 5.9x

And Job B pays $7.20 per hour

Therefore,

Amount receive from Job B = 7.20y

Also it is given that, he work at each job the week that he made $197.80

Therefore,

5.90x + 7.20y = 197.8 ....(ii)

Now multiplying equation (i) by 5.9 we get,

5.90x + 5.90y = 177 ....(iii)

Subtracting equation (ii) and equation (iii) we get,

1.3y = 20.8

Dividing both the side by 1.3 we get,

1.3y/1.3 = 20.8/1.3

Solving we get,

y = 16

Putting the value of y in equation (i) we get,

x + 16 = 30

Subtracting both the side by 16 we get,

x + 16 - 16 = 30 - 16

Solving we get,

x = 14

Thus, we get

x = 14

y = 16

Hence,

Number hours that Joe worked at job A in a week = 14 hours

and,

Number hours that Joe worked at job B in a week = 16 hours

Thus, Joe worked for 14 hours at Job A and for 16 hours at Job B.

To learn more about simultaneous equations :

https://brainly.com/question/16763389

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