2/5 of my sister's beads are yellow, 7/13 of the remaining beads are green. The rest of the beads are black. If there are 32 more yellow beads than black beads, how many beads are green.
total number of beads --- x
yellows ----- (2/5)x = 2x/5
remaining: 3x/5
green ---- (7/13)(3x/5) = 21x/65
rest are black.
black = x - 21x/65 - 2x/5
= 65x/65 - 21x/65 - 26x/65
= 18x/65
yellow = blacks + 32
2x/5 = 18x/65 + 32
times 65 , the LCD
26x = 18x + 2080
8x = 2080
x = 260
so subbing in my definitions
104 are yellow, 84 are green and 72 are black
check:
-- are there 32 more yellows than blacks ?? , YES
To find out how many beads are green, we first need to find the total number of beads.
Let's assume the total number of beads is "x".
We are given that 2/5 of the sister's beads are yellow. So, the number of yellow beads can be calculated as (2/5) * x.
We are also given that there are 32 more yellow beads than black beads. So, the number of black beads can be calculated as (2/5) * x - 32 (since there are 32 fewer black beads than yellow beads).
Now, we are given that 7/13 of the remaining beads are green. Since the remaining beads are the ones that are neither yellow nor black, the number of green beads can be calculated as (7/13) * (x - [(2/5) * x] - [(2/5) * x - 32]).
Simplifying the equation:
Green beads = (7/13) * (x - (2/5) * x - (2/5) * x + 32)
Green beads = (7/13) * (x - (4/5) * x + (4/5) * x - 32)
Green beads = (7/13) * (x - 64)
However, we don't know the value of "x" yet. To find that, we need additional information or another equation.