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.
To solve this problem, we can use a trial and error approach. We will start by assuming a number for the blue umbrellas and use the given ratios to find the number of each color.
Let's assume the number of blue umbrellas sold was "x."
According to the information given:
- The number of red umbrellas sold is five times the number of blue umbrellas. Therefore, the number of red umbrellas sold is 5x.
- The number of green umbrellas sold is three times the number of blue umbrellas. Therefore, the number of green umbrellas sold is 3x.
- The number of black umbrellas sold is nine more than the number of blue umbrellas. Therefore, the number of black umbrellas sold is x + 9.
- The number of purple umbrellas sold is seven fewer than the number of black umbrellas. Therefore, the number of purple umbrellas sold is (x + 9) - 7, which simplifies to x + 2.
- We know that five umbrellas were purple, so x + 2 = 5. This implies that x = 3.
Now that we have the value of x, we can find the number of each color:
- Blue: x = 3
- Red: 5x = 5 * 3 = 15
- Green: 3x = 3 * 3 = 9
- Black: x + 9 = 3 + 9 = 12
- Purple: x + 2 = 3 + 2 = 5
- White: We know that six umbrellas were white, so the remaining umbrellas (50 - 3 - 15 - 9 - 12 - 5 - 6) were white. This simplifies to 50 - 3 - 15 - 9 - 12 - 5 - 6 = 50 - 50 = 0.
Therefore, the number of each color of umbrellas sold is:
- Blue: 3
- Red: 15
- Green: 9
- Black: 12
- Purple: 5
- White: 0