A jar contains red, blue and yellow marbles.The number of red marbles is ten more than the number of yellow marbles and the number of blue marbles is double the number of yellow marbles. If the probability of choosing a yellow marble is one-fifth , how many marbles are in the jar?
yellow marbles ---- x
blue marbles ------ 2x
red marbles ------- x+10
total = 4x + 10
prob to choose a yellow = x/(4x+10) = 1/5
5x = 4x+10
x = 10
10 yellows , 20 blues, and 20 reds for a total of 50 marbles
To determine the number of marbles in the jar, we can use algebraic equations based on the given information.
Let's assume the number of yellow marbles is "x".
According to the given information:
- The number of red marbles is ten more than the number of yellow marbles, so the number of red marbles is "x + 10".
- The number of blue marbles is double the number of yellow marbles, so the number of blue marbles is "2x".
The total number of marbles in the jar is the sum of the red, blue, and yellow marbles:
Total marbles = red marbles + blue marbles + yellow marbles
Total marbles = (x + 10) + 2x + x
Total marbles = 4x + 10
Given that the probability of choosing a yellow marble is one-fifth (1/5), we can set up the following equation:
Probability of choosing yellow marble = Number of yellow marbles / Total number of marbles
1/5 = x / (4x + 10)
To solve the equation and find the value of "x", we can cross-multiply:
x = (1/5) * (4x + 10)
x = (4/5)x + 2
(1/5)x = 2
x = 2 * 5
x = 10
Now that we have found the value of "x" as 10, we can substitute it back into our equation to find the total number of marbles:
Total marbles = 4x + 10
Total marbles = 4 * 10 + 10
Total marbles = 40 + 10
Total marbles = 50
Therefore, there are 50 marbles in the jar.