Problem Solving

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the 2 discount rates is 22%, what is the discount rate on Pony jeans?

(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%

The answer is B...don't know how that comes out...

Let the rates of discount on Fox and Pony Jeans be x and y respectively

x + y=22 ----- 1)

Using the 2 discounts the customer saves $9

So 15*3x/100 + 18*y/100 = 9
45x + 36y = 900
5x + 4y = 100 ------ 2)

Now when you solve the 2 you will get y = 10%. Discount on Pony's jeans = 10%

Let the discount rates on fox jeans and Pany jeans be 'm' and 'n' respectively.
Also, let the actual selling prices after discounting be 'x' and 'y' for fox and pony jeans respectively.
Without Discounts,
Three fox jean and two pony jeans cost
=3($15)+2($18)
=$81
With discounts, $9 dollar is saved.
Actual total selling price
=$(81-9)= $72
This also implies that : 3x+2y=72
The actual selling prices are the original price minus the amount of the discounts.
x= 15 - (15* $$\frac{m}{100}$$ )
15-0.15m
and y= 18-(18* $$\frac{n}{100}$$ )
18-0.18n
Putting these expressions for x and ynin
3x+2y=72
i.e 3(15-0.15m)+ 2(18-0.18n)=72
45-0.45m+36-0.36n=72
0.45m+0.36n=9....eqn 1
From the question
The discount add up to 22%
i.e m+n =22
m=22-n
substituting 22-n for m in eqn 1
0.45(22-n) + 0.36n=9
9.9-0.45n+0.36n=9
0.09n=0.9
Therefore, n=
$$\frac{0.9}{0.09}$$ =10
Since, n represents the discount rate on pony jeans thus rate = 10%.