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Mia worked 2 part time jobs for a total of 25 hours per week. She wrote and solved the following equation to determine how many hours she worked at each job during a week and which she earned $301. the equation 10x + 13y = 301 The choices A $104, $197 B. $80, $221 C. $91, $110 D. $141, $160

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Answer: $80, $221 (Option B)

 

 

WORKINGS

 

Mia worked 2 part time jobs for a total of 25 hours per week.

Assume,

She works on the first Job for x hours

She works on the second job for y hours

Then x + y = 25            (Equation I)

 

We are told that in a week, she earned $301

This pay is represented by the equation 10x + 13y = 301            (Equation II)

 

Now, we have:

x + y = 25            (Equation I)

10x + 13y = 301            (Equation II)

 

Solving for x and y;

Divide equation 2 by 10

10x + 13y = 301            (Equation II)

10x/10 + 13y/10 = 301/10

x + 1.3y = 30.1             (Equation III)

 

Subtract Equation I from Equation III

x + 1.3y – (x + y) = 30.1 – 25

x + 1.3y – x – y = 5.1

 

Collect like terms’

x – x + 1.3y – y = 5.1

0.3y = 5.1

 

Divide through by 0.3

0.3y/0.3 = 5.1/0.3

y = 17

 

Substitute 17 for y in equation I

x + y = 25            (Equation I)

y = 17

x + 17 = 25

 

Subtract 17 from both sides of the equation

x + 17 – 17 = 25 – 17

x = 8

 

Therefore,

x = 8, y = 17

This means that,

She works on the first Job for 8 hours

She works on the second job for 17 hours

 

 

Now, her pay is represented by the equation 10x + 13y = 301

This means,

She is paid $10 per hour on the first job

She is paid $13 per hour on the second job

 

If she is paid $10 per hour on the first job

She works on the first Job for 8 hours

This means, she earned $10 x 8 on the first Job

= $80

 

If she is paid $13 per hour on the second job

She works on the second job for 17 hours

This means, she earned $13 x 17 on the second Job

= $221

 

The answer is $80, $221 (Option B)

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