Ali has some blue, red and green stickers. 2/9 of the stickers and another 20 stickers are blue. 1/3 of the remaining stickers and another 60 stickers are
red. The rest of the stickers are green. There are 90 green stickers.
(a) How many red stickers does Ali have?
(b) Find the total number of stickers Ali has.
If there are x stickers,
blue = 2/9 x + 20
red: 1/3 (x - (2/9 x + 20)) + 60
green: the rest
so, that means
2/9 x + 20 + 1/3 (x - (2/9 x + 20))+60 + 90 = x
x = 315
so red = 135
Let's solve this step-by-step:
(a) To find the number of red stickers, we need to find the number of stickers remaining after the blue stickers are accounted for. We know that 2/9 of the stickers and another 20 stickers are blue, so the total number of blue stickers can be calculated as:
(2/9) * total stickers + 20 = number of blue stickers
Since we know that the total number of green stickers is 90, we can substitute it into the equation:
(2/9) * total stickers + 20 = 90
Now, let's solve for the total number of stickers:
(2/9) * total stickers = 90 - 20
(2/9) * total stickers = 70
total stickers = (70 * 9) / 2
total stickers = 315
Now, substitute the total number of stickers back into the equation to find the number of red stickers:
(1/3) * total stickers + 60 = number of red stickers
(1/3) * 315 + 60 = number of red stickers
105 + 60 = number of red stickers
number of red stickers = 165
So, Ali has 165 red stickers.
(b) The total number of stickers Ali has can be calculated by summing up the number of blue, red, and green stickers:
Total stickers = number of blue stickers + number of red stickers + number of green stickers
Total stickers = 20 + 165 + 90
Total stickers = 275
Therefore, Ali has a total of 275 stickers.
To solve this problem, we can break it down step by step:
Let's start by finding the number of blue stickers Ali has.
According to the information given, 2/9 of the stickers and another 20 stickers are blue. This means that 2/9 of the stickers can be represented as 20.
Let's represent the total number of stickers as x.
2/9 * x + 20 = blue stickers
Simplifying the equation:
2/9 * x = blue stickers - 20
Now, let's solve for x:
x = (blue stickers - 20) * 9/2
Since we know that there are 90 green stickers, we can subtract the number of blue and green stickers from the total number of stickers to find the number of red stickers.
Now, let's find the number of red stickers.
The number of blue and green stickers is already known:
blue stickers = (blue stickers - 20) * 9/2
green stickers = 90
The equation to find the number of red stickers becomes:
red stickers = total stickers - (blue stickers + green stickers)
Finally, let's find the total number of stickers by summing the number of blue, red, and green stickers:
total stickers = blue stickers + red stickers + green stickers
By substituting the given values into these equations, we can find the answers to the questions:
(a) How many red stickers does Ali have?
Substitute the values into the equation for red stickers.
(b) Find the total number of stickers Ali has.
Substitute the values into the equation for the total number of stickers.