Joan sold half of her comic books and then bought 8 more. She now has 15. How many did she begin with?

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Answer 1 · 2016-11-01T14:11:42

$14$ $14$

Let's construct an equation for the question and solve it

Let the number of comic books that Joan had in the beginning is $x$ $x$

In the start she sold half her books (so,multiply by $\frac{1}{2}$ $1/2$ )

$x \cdot \frac{1}{2}$ $color(red)(x*1/2$

Next, she bought $8$ $8$ more books (so,add $8$ $8$ )

$x \cdot \frac{1}{2} + 8$ $color(red)(x*1/2+8$

At the last she has $15$ $15$ books (so,let the equation equal $15$ $15$ )

$x \cdot \frac{1}{2} + 8 = 15$ $color(red)(x*1/2+8=15$

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Now let's solve the completed equation

$\to x \cdot \frac{1}{2} + 8 = 15$ $rarrx*1/2+8=15$

Subtract $8$ $8$ both sides

$rarrx*1/2+cancel8-cancelcolor(violet)(8)=15-color(violet)(8)$

$rarrx*1/2=7$

Multiply both sides by $2$

$rarrx*1/cancel2*cancelcolor(violet)(2)=7*color(violet)(2)$

$color(green)(rArrx=14$

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So Joan started with $14$ comic books

Hope this helps !...

:)