math
posted by Jas on .
Fifty umbrellas were sold on a rainy April day. Five times as many
red as blue were sold, three times as many green as blue, nine more
black than blue, and seven fewer purple than black. Five umbrellas
were purple and six were white. How many of each color were sold?

Break it down according to what you know, then you will be able to figure it out. Here is what we know. A good base will be blue, since there is much based off of it.
x = blue
5x = red
3x = green
x + 9 = black
x + 2 = purple
6 = white
You know purple is 5, so figure out x, then you can do the rest. 
Red = 5Blue
Green = 3Blue
Black = Blue + 9
Purple = Black  7
Purple = Blue + 9  7
Purple = Blue + 2
But Purple = 5
Blue + 2 = 5
Blue = 3
then Red = 15
Green = 9
Black = 11
Black = 4
Purple = 5
White = 6
check: 15+9+11+4+5+6 = 50 
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UMBRELLAS
White = 6
Blue = x
Red = 5x
Green = 3x
Black = x + 9
Purple = x + 2
The equation...
6 + x + 5x + 3x + x + 9 + x + 2 = 50
We know that purple is 5 so...
x + 2 = 5
x = 5  2
x = 3
Now we know that x = 3.
This is the problem we started off with
6 + x + 5x + 3x + x + 9 + x + 2 = 50
now just plug in x...
6 + 3 + 5(3) + 3(3) + (3) + 9 + (3) + 2 = 50
6 + 3 + 15 + 9 + 12 + 5 = 50
50= 50
So this is correct
White = 6
Blue = 3
Red = 15
Green = 9
Black = 12
Purple = 5
There are 6 white, 3 blue, 15 red, 9 green, 12 black, and 5 purple umbrellas.