In a container, there are candies of 3 colors, yellow, white and purple. There are 108 more white candies than purple candies. The number of purple candies is 1/2 more than the yellow candies. Given that the number of purple candies is 24% of the total number of candies in the container, how many more white candies are there than yellow candies?
200 👍 0 👎 👁 10,000 🚩
so, what do you know?
w = p+108
p = 3/2 y
p = .24(w+p+y)
solve, then find w-y
post your work if you get stuck
w = p + 108
p = y + y/2 so y = 2 p/3
p = ( 24/100)(w + y + p)
100 p = 24 w +24 y + 24 p
76 p = 24 w + 24 y
76 p = 24 (p+108) + 24(2 p/3)
76 p = 24 p + 2592 +16 p
36p = 2592
p = 72
Your turn :)
Yup
To solve this problem, we need to analyze the given information step by step.
Let's represent the number of yellow candies as 'y,' the number of white candies as 'w,' and the number of purple candies as 'p.'
1. From the statement, we know that the number of white candies is 108 more than the number of purple candies:
w = p + 108
2. We also know that the number of purple candies is 1/2 more than the number of yellow candies:
p = y + (1/2)y
p = (3/2)y
3. Furthermore, we are given that the number of purple candies is 24% of the total number of candies in the container:
p = 0.24(y + w + p)
Now, we can use these equations to find the values of y, w, and p.
Substituting the value of p from equation 2 into equation 3, we have:
(3/2)y = 0.24(y + w + (3/2)y)
Simplifying this equation:
(3/2)y = 0.24(5/2)y + 0.24w
(3/2)y = (3/10)y + 0.24w
Multiplying both sides by 10 to get rid of the fractions:
15y = 3y + 2.4w
Rearranging the equation:
12y = 2.4w
Dividing both sides by 2.4, we get:
5y = w
This means that the number of white candies is 5 times the number of yellow candies.
Now, to find the difference between white and yellow candies, we can substitute the value of w from equation 1 into the above equation:
5y = p + 108
Substituting the value of p from equation 2, we have:
5y = (3/2)y + 108
Subtracting (3/2)y from both sides:
(7/2)y = 108
Dividing both sides by (7/2), we find:
y = (2/7) * 108 = 30
Therefore, the number of yellow candies is 30.
To find the number of white candies, we multiply the number of yellow candies by 5:
w = 5 * 30 = 150
The difference between white and yellow candies is:
w - y = 150 - 30 = 120
So, there are 120 more white candies than yellow candies in the container.