A student works part-time as a tutor and a cashier. As a tutor, they earn $15 per hour, and as a cashier, they earn $12 per hour. If they work 20 hours and earn $270, what system of equations represents this scenario?
a. $15x+12y=270, x+y=20$
b. $15x+12y=20, x+y=270$
c. $12x+15y=270, x+y=20$
d. $12x+15y=20, x+y=270
Answer (2)
Define variables: Let x be the hours tutoring and y be the hours as a cashier.
Write the earnings equation: 15 x + 12 y = 270 .
Write the hours equation: x + y = 20 .
The system of equations is 15 x + 12 y = 270 and x + y = 20 , which matches option a. 15 x + 12 y = 270 , x + y = 20
Explanation
Define variables Let x be the number of hours the student works as a tutor, and y be the number of hours the student works as a cashier. We can set up a system of equations based on the given information.
Equation for total earnings The student earns $15 per hour as a tutor and $12 per hour as a cashier, and their total earnings are $270 . This can be represented by the equation: 15 x + 12 y = 270
Equation for total hours The student works a total of 20 hours. This can be represented by the equation: x + y = 20
System of equations and answer Therefore, the system of equations that represents this scenario is: 15 x + 12 y = 270 x + y = 20 This corresponds to option a.
Examples
Understanding systems of equations is crucial in many real-world scenarios. For example, imagine you are planning a balanced diet. You need to meet certain nutritional requirements (like calories and protein) by combining different types of food. Each food has a different amount of calories and protein per serving. By setting up a system of equations, you can determine the exact amount of each food you need to eat to meet your nutritional goals. This is just one example of how systems of equations can help you make informed decisions in everyday life.
The system of equations representing the student's work situation is given by 15 x + 12 y = 270 for earnings and x + y = 20 for total hours. The correct option is (a).
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