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?

Answer 1

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.
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Answer 2

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.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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