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?
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Step 1
Suppose Maya has B black beads and so has 2B white beads.
so she was left with $\left(B-5\right)$ black beads and $2B-40$ white beads.
Now as she has 3 times as many black beads as white,
$B-5=3\ast \left(2B-40\right)$
or
$B-5=6B-120$
or
$120-5=6B-B$
or
$5B=115$ i.e. $B=\frac{115}{5}=23$
Hence, she started with 23 black beads.