Maya has 2x as many white beads as black beads. After using 40 white and 5 black to make a necklace she has 3x as many black beads as white. How many black beads she started with?

Question

Cameron Arnold · Accepted Answer

She started with #23# black beads.

Suppose Maya has #B# black beads and so has #2B# white beads. She used #5# black beads and #40# white beads, so she was left with #(B-5)# black beads and #2B-40# white beads. Now as she has #3# times as many black beads as white, #B-5=3xx(2B-40)# or #B-5=6B-120# or #120-5=6B-B# or #5B=115# i.e. #B=115/5=23# Hence, she started with #23# black beads.

Jeremiah Andrews · Answer

undefined Let's denote the initial number of black beads as $ b $ and the initial number of white beads as $ w $.

Given:
1. Maya has 2 times as many white beads as black beads, so we can write $ w = 2b $.
2. After using 40 white beads and 5 black beads to make a necklace, Maya has 3 times as many black beads as white, so we can write $ b - 5 = 3(w - 40) $.

Now, we can substitute the value of $ w $ from the first equation into the second equation:

$$ b - 5 = 3(2b - 40) $$

Solve this equation for $ b $:

$$ b - 5 = 6b - 120 $$
$$ 120 - 5 = 6b - b $$
$$ 115 = 5b $$
$$ b = 23 $$

So, Maya started with 23 black beads.