Suzie's Discount Footwear sells all pairs of shoes for one..

[AAPL]

Suzie's Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suzie's Discount Footwear?

A. $2.5
B. $5.00
C. $5.50
D. $7.50
E. $15.00

The OA is B.

Price for Shoes = x

Price for Boots = y

$$22x+16y=650\ \ (1)$$
and
$$8x+32y=760\ \ (2)$$
Then, from the two equations above we get,

from (1)
$$x=\frac{650-16y}{22}$$
then, x into (2)
$$8\left(\frac{650-16y}{22}\right)+32y=760\ \Rightarrow y = 20$$
then, y=20 into x equation,
$$x=15$$
Finally,
$$y-x=5$$
Is there a strategic approach to this PS question? Can any experts help me, please?

[mbawisdom]

Suzie's Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suzie's Discount Footwear?

A. $2.5
B. $5.00
C. $5.50
D. $7.50
E. $15.00

The OA is B.

Price for Shoes = x

Price for Boots = y

$$22x+16y=650\ \ (1)$$
and
$$8x+32y=760\ \ (2)$$
Then, from the two equations above we get,

from (1)
$$x=\frac{650-16y}{22}$$
then, x into (2)
$$8\left(\frac{650-16y}{22}\right)+32y=760\ \Rightarrow y = 20$$
then, y=20 into x equation,
$$x=15$$
Finally,
$$y-x=5$$
Is there a strategic approach to this PS question? Can any experts help me, please?

I set it up in a similar way:

S = price for shoes
B = price for boots

(1) 22S + 16B = 650
(2) 8S + 32B = 760

Let's multiply (1)*2 so that we can easily get rid of the B's:
(3) 44S + 32B = 1300

Let's subtract (3) - (2):
36S = 540
S = 15

Plus S=15 into (2):
8*15 +32B = 760
120 + 32B = 760
32B = 640
B = 20

B - S:
20 - 5 = 5

[Jeff@TargetTestPrep]

Suzie's Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suzie's Discount Footwear?

A. $2.5
B. $5.00
C. $5.50
D. $7.50
E. $15.00

We can let h and b = the price per pair of shoes and boots, respectively, and create the equations:

22h + 16b = 650

11h + 8b = 325 (Eq. 1)

and

8h + 32b = 760

h + 4b = 95 (Eq. 2)

Multiplying Eq. 2 by -2 we have:

-2h - 8b = -190 (Eq. 3)

Adding Eq. 1 and Eq. 3 we have:

9h = 135

h = 15

Substituting h = 15 into Eq. 2 we have:

15 + 4b = 95

4b = 80

b = 20

Thus a pair of boots costs 20 - 15 = 5 dollars more than a pair of shoes.

Answer: B