The ratio of Maya's beads to Kayla's beads was12:7. After Maya bought another 28 beads and Kayla gave away 32 beads, 5/7 of Kayla's beads were left. How many more beads did Maya have than Kayla in the beginning? Find the ratio of Maya's beads to Kayla's beads?
m/k = 12/7
k-32 = 5/7 k
so, 2/7 k = 32
k = 112
m/112 = 12/7
m = 192
so, in the beginning
m-k = 80
Maya had 80 more beads than Kayla
Now,
(m+28)/(k-32) = 220/80 = 11/4
Thanks!,
But where did the 200 come from?
220*
To find out how many more beads Maya had than Kayla in the beginning, let's first calculate the number of beads each of them had initially.
Let's assume that Maya had 12x beads and Kayla had 7x beads.
After Maya bought another 28 beads, she had a total of (12x + 28) beads.
After Kayla gave away 32 beads, she had (7x - 32) beads.
According to the given information, 5/7 of Kayla's beads were left, so we can set up the following equation:
(7x -32) = (5/7) * (7x)
To solve this equation, we can cross-multiply:
7x - 32 = 5x
Subtracting 5x from both sides of the equation gives:
2x = 32
Dividing both sides of the equation by 2 gives:
x = 16
Now we can substitute the value of x back into the initial number of beads:
Maya had 12x beads = 12 * 16 = 192 beads.
Kayla had 7x beads = 7 * 16 = 112 beads.
Therefore, initially Maya had 192 - 112 = 80 more beads than Kayla.
The ratio of Maya's beads to Kayla's beads in the beginning is 192:112, which simplifies to 12:7.