vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. what is the equation that can be used to find the value of y, the total time that vlad spent on his homework, and what are the constraints on the values of x and y?
vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. what is the equation that can be used to find the value of y, the total time that vlad spent on his homework, and what are the constraints on the values of x and y?
Answer: Let’s break down the information provided:
- Vlad spent 20 minutes on his history homework.
- He solved x math problems, and each math problem took 2 minutes to complete.
To find the total time Vlad spent on his homework (y), we can create an equation:
y = 20 minutes (history homework) + 2 minutes per math problem (2x)
Now, simplify the equation:
y = 20 + 2x
In this equation, y represents the total time Vlad spent on his homework, and x represents the number of math problems he solved.
Constraints:
- The number of math problems, x, should be a whole number (you can’t solve a fraction of a math problem).
- Both x and y should be non-negative values (time cannot be negative).
- Since Vlad spent at least 20 minutes on history homework, y should be greater than or equal to 20 minutes.
So, the equation to find the total time Vlad spent on his homework is y = 20 + 2x, and the constraints are that x should be a non-negative whole number, y should be greater than or equal to 20, and both x and y cannot be negative.