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2 months ago

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Maia had 2064 more beads than Jenny. After Maia used 144 beads to make a necklace, she had 5 times as many beads as Jenny. A) ho

w many more beads did Maia have than Jenny in the end? How many beads did Maia have at first?

1 answer:

tester [12.3K]2 months ago

3 0

Answer:

A) Maia had 1920 beads more.

B) Maia had 2544 beads at first.

Step-by-step analysis:

Let x denote the beads with Jenny and y for Maia.

The information provided states that Maia possesses 2064 beads more than Jenny, which can be represented mathematically as:

$y=x+2064...(1)$

Additionally, after Maia made a necklace with 144 beads, she had five times more beads than Jenny.

This can also be formulated as an equation:

$y-144=5x...(2)$

A) Since Maia had 2064 beads more than Jenny before using 144 beads, we calculate her final bead count by subtracting 144 from 2064.

$\text{Number of beads Maia had more than Jenny in the end}=2064-144$

$\text{Number of beads Maia had more than Jenny in the end}=1920$

Thus, Maia is left with 1920 beads more than Jenny.

B) To solve this system of linear equations, we will utilize the substitution method.

By inserting equation (1) into equation (2), we arrive at:

$x+2064-144=5x$

$x+1920=5x$

$x-x+1920=5x-x$

$1920=4x$

Now, let's divide our equation by 4.

$\frac{1920}{4}=\frac{4x}{4}$

$480=x$

Now, we'll substitute x=480 into equation (1) to isolate y.

$y=480+2064$

$y=2544$

Conclusively, Maia initially had 2544 beads.

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