How would I set up this problem to solve it:
Gene offers 30 mins. and 60 mins. driving lessons. He gave 8 lessons that lasted 7 hours. How many 60 minute lessons did he give?
well six one hours plus 2 half hours = 7 hours
What is the equation for this problem
Corrected the question from earlier
If you have a line intersecting at (3,6). what equation would represent both lines?
To solve this problem, you can set up a system of equations. Let's call the number of 30-minute lessons x, and the number of 60-minute lessons y.
According to the problem, Gene gave a total of 8 lessons. So the first equation is:
x + y = 8
Next, we know that each 30-minute lesson lasts for half an hour, and each 60-minute lesson lasts for a full hour. So the total amount of time for the 30-minute lessons is 0.5x hours, and the total amount of time for the 60-minute lessons is 1y hour. The equation representing the total time is:
0.5x + 1y = 7
Now, you have a system of two equations:
x + y = 8
0.5x + 1y = 7
You can solve this system of equations using various methods such as substitution or elimination. I will solve it using the elimination method.
First, let's multiply the first equation by 0.5 to make the coefficients of x in both equations the same:
0.5(x + y) = 0.5(8)
0.5x + 0.5y = 4
Now, subtract the second equation from the new first equation:
(0.5x + 0.5y) - (0.5x + 1y) = 4 - 7
0.5x + 0.5y - 0.5x - y = -3
-0.5y = -3
To solve for y, divide both sides of the equation by -0.5:
-0.5y / -0.5 = -3 / -0.5
y = 6
Therefore, Gene gave 6 lessons that lasted 60 minutes.