Question

Help please!! Thanks

Answer 1

Answer:

A

Step-by-step explanation:

First, let's label the variables:

$\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}$

The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.

In other words, the total Lou now has is:

$L=(\frac{1}{2}x )+(x-2)$

The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).

Simplifying, we get:

$L=\frac{3}{2}x-2$

Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:

$I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)$

The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:

$I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6$

Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:

$37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)$

The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:

$37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36$