Carter has a large marble collection. Carter knows that he has exactly 20 blue marbles in his collection, but does not know how many marbles he has in all. Carter mixes up his marbles and randomly selects 40 marbles. Of the 40 marbles that he chose, 4 were blue. How many marbles does Carter have in total? You MUST explain your reasoning
4/40 = 0.1
0.1x = 20
x = 200
Since 4 of 40 marbles were blue, we assume that about 10% of his total marbles are are blue.
10% of 200 is 20.
To find out the total number of marbles Carter has, we need to set up an equation using the information given.
Let's assume that Carter has "X" total marbles in his collection. We know that out of these X marbles, 20 are blue.
When Carter randomly selects 40 marbles, he finds that 4 of them are blue.
Since the selected marbles represent a random sample of the entire collection, we can set up a proportion to solve for X.
We can create the proportion:
(Blue marbles in the sample) / (Total marbles in the sample) = (Blue marbles in the collection) / (Total marbles in the collection)
Plugging in the values we know, we get:
4 / 40 = 20 / X
To solve for X, we can cross-multiply:
4 * X = 40 * 20
4X = 800
Dividing both sides of the equation by 4, we get:
X = 800 / 4
X = 200
Therefore, Carter has 200 marbles in total.