Question

Each of the pair of shoes available in a store is either
Reebok or Adidas. Due to off season 10% of the
Reebok and 15% of the Adidas shoes were on sale.
What percentage of the store's stock was that of
Adidas shoes, if total 12% of the store's stock was
on sale?​

Answer 1

Step-by-step explanation:

solution is attached

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Answer 2

40% of the store's stock was that of  Adidas shoes

Step-by-step explanation:

Consider total stock of Reebok shoes = x pairs,

And, Adidas shoes = y pairs,

∵ 12% of the store's stock was on sale,

So, pairs of shoes which are on sale = 12% of (x+y) = 0.12(x+y),

Now, 10% of the  Reebok shoes are on sale,

i.e. Reebok shoes which are on sale = 10% of x = 0.1x

Also, 15% of the Adidas shoes were on sale,

i.e. Adidas shoes  which are one sale = 15% of y = 0.15y,

Thus,

0.10x + 0.15y = 0.12(x+y)

0.10x + 0.15y = 0.12x + 0.12y

0.03y = 0.02x

$\implies y =\frac{0.02}{0.03}x=\frac{2x}{3}$

So, total shoes = x + y = $x + \frac{2}{3}x=\frac{3x+2x}{3} =\frac{5x}{3}$,

Hence, the percentage of the store's stock was that of Adidas shoes

$=\frac{y}{x+y}\times 100$

$=\frac{2x/3}{5x/3}\times 100$

$=\frac{200}{5}$

= 40%

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