Hi :)
The mean is the average, and to take the average, they had to do this:
{students' minutes added together} ÷ 14 students = 133 minutes
This is basic pre-algebra; to find the total, we do the reverse of what they did. Since they divided by 14 to get 133, we're going to do the opposite. We're going to multiply 133 by 14 to get the total:
133 × 14 = 1862 minutes
Next question. The typical amount of time a student talked in a week was 133, and you're trying to find the typical amount of time in a day. There are 7 days in a week, so divide 133 by 7 to get the typical number of minutes in a day. (I won't do this for you-- you got this!)
Alright, so 19 students talked 171 minutes on average. Let's go back again and see what the total number of minutes were.
{total} ÷ 19 = 171
{total} = 171 × 19
{total} = 3249
But, hang on. They don't just want to know the total, they want to know the "mean number of minutes the additional five other students talked". That means we have to first subtract the 14 students' total from the 19 students' total to see what the difference is:
3249 - 1862 = 1387
So the five students added 1387 minutes to the average.
Divide 1387 by 5 to see the mean number of minutes per each of the five students.
You got this! Have fun!!
There should be a horizontal line at where y=4. everything in the bottom left between the lines should be shaded
X=-2 and y=3.
The first step we take is to substitute the value for y from the second equation into the first equation:
4x+5(3x+9)=7
This is justified by substitution. The next step is:
4x+5*3x+5*9=7
4x+15x+45=7
This is justified by the distributive property. The next step is:
19x+45=7
This is justified by addition of like terms. The next step is:
19x+45-45=7-45
19x=-38
This is justified by the subtraction property of equality. The next step is:
19x/19 = -38/19
x=-2
This is justified by the division property of equality. The next step is:
y=3(-2)+9
y=-6+9
y=3
This is justified by substitution, multiplication and addition, in that order.
Answer:
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