Mitch collects sports cards he has 16 baseball cards 33 basketball cards and 20 football cards he places all of his sports cards in a large album each page of the album will hold nine cards Mitch completely fills a page with sports cards before filling the next page he continues filling pages until he runs out of cards how many pages does he need to hold his collection of sports cards how many sports cards will be on the last page and if Mitch put all the same kind of cards on pages how many pages would he need for his baseball cards

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CameronVand21

10.09.2020

Mathematics

1. let r be the point with unknown x-coordinate. consider vectors $\overrightarrow{qr}=())=(x+14)$ and $\overrightarrow{rs}=(2-x).$

these vectors are colinear and

$\dfrac{\overrightarrow{qr}}{\overrightarrow{rs}}=\dfrac{3}{5}.$

then

$\dfrac{x+14}{2-x}=\dfrac{3}{5},\\ \\5(x+14)=3(2-x),\\\\5x+70=6-3x,\\\\8x=-64,\\\\x=-8.$

2. if you need correct formula, then

$\dfrac{x_r-x_q}{x_s-x_r}=\dfrac{m}{n},\\ \\n(x_r-x_q)=m(x_s-x_r),\\\\nx_r-nx_q=mx_s-mx_r,\\\\x_r(n+m)=mx_s+nx_q,\\\\x_r=\dfrac{mx_s+nx_q}{m+n}.$

answer: point r partitions the directed line segment from q to s in a m: n, the ratio to determine point r is

$x_r=\dfrac{mx_s+nx_q}{m+n}.$

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