Answer: This is gonna be a long one
1)Winston grows green dragon apples. This year, he shipped 80%of these apples to sell at supermarkets and kept the rest to make cider. Of all the green dragon apples he sold to the supermarkets, only 60% of them were bought. If a total of 420 green dragon apples were bought, how many green dragon apples did Winston keep to make cider?
Call the number he shipped to the store, N
So
.
60N = 420 divide both sides by ,60
420 / .60 = N = 700 were shipped to the stores
But this number was 80% of the total he grew = T
So
.80T = 700 divide both sides by .80
700/.80 = T = 875
But..he kept 20% of these = 875 * .20 = 175
2)Ms. Forsythe gave the same algebra test to her three classes. The first class averaged 80%, the second class averaged 85%, and the third 89%. Together, the first two classes averaged 83%, and the second and third classes together averaged 87%. What was the average for all three classes combined? Express your answer to the nearest hundredth.
The average = total points / number of students
So....total points = average*number of students
Let the total number of students in each class = x , y and z
The total number of points the first class amassed was 80x
The total number of points amased by the second class was 85y
The total number of points amassed by the third class = 89z
So...for the first two classes we have
[ 80x + 85y ] / [ x + y] = 83
80x + 85y = 83x + 83y subtract 80x, 83y from both sides
3x = 2y
x = 2/3y
And,,,for the second two classes we have
[ 85y + 89z ] / [ y + z ] = 87
[ 85y + 89z ] = 87 [y + z]
85y + 89z = 87y + 87z subtract 85y, 87z from both sides
2z = 2y
y = z
So...for the three classes.....
Total points by all three classes / number of class members = the average for all three classes
[ 80x + 85y + 89z ] / [ x + y + z ] =
[sub for x and z ]
[80 (2/3)y + 85y + 89y] / [ (2/3)y + y + y ]
y [ 80 (2/3) + 85 + 89 ] / [ y [( 2/3) + 1 + 1] ] [cancel the y's ]
[ 80 (2/3) + 85 + 89] [ 8/3 ]
[ 160/3 + 85 + 89 ] / [8/3] =
[ 160/3 + 255/3 + 267/3] / [8/3] multiply top/bottom by 3
[160 + 255 + 267 ] / 8 =
85.25 = average for all three classes
Step-by-step explanation:
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