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calculus

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by stephny » Tue Nov 12, 2013 3:12 am
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 22pairs of shoes and 16pairs of boots for $650. On Tuesday, the store sold 8pairs 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?
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Source: — Problem Solving |
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by theCodeToGMAT » Tue Nov 12, 2013 3:35 am
Shoes per pair = S
Boots per pair= B

On Monday:
22S + 16B = 650 -(1)

On Tuesday:
8S + 32B = 760 -(2)

To find: B-S


Multiply (1) by 2

44S + 32B = 1300
8S + 32B = 760
______________
36S = 540
S = 540/36 = 15

PUTTING IN (2)
8(15) + 32B = 760

32B = 760 - 120
32B = 640
B = 20

Hence, 20-15 = "5"
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by Mathsbuddy » Tue Nov 12, 2013 5:35 am
Nearly identical to the previous demonstration:

22s + 16b = 650 (equation 1)
8s + 32b = 760 (equation 2)

Half of equation 2 gives:

4s + 16b = 380 (equation 3)

Subtracting equation 3 from equation 1 gives:

18s = 270
so s = 15

as before, substituting s = 15 into any other equation gives

b = 20

Therefore b - s = 20 - 15 = 5

So the answer is £5.

Nonetheless, I question why is this problem called "calculus"?
These are simultaneous equations; just pure algebra without any calculus.
Calculus requires change. The prices are fixed.
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by [email protected] » Tue Nov 12, 2013 2:04 pm
Hi stephny,

Both Rahul and Mathsbuddy have provided correct math explanations for this question, so I won't rehash that here.

It's worth noting that this type of question is called "system math" and it shows up on the GMAT a number of times. The standard "system" question will look just like this one: a word problem that has two equations within it (that you have to translate). The two equations will be based on two variables; the phrase "2 variables, 2 unique equations...I can solve it" is a phrase that you should get comfortable with.

Sometimes system questions won't be story problems and sometimes they'll be more complex (3 variables and 3 unique equations, for example). In all cases, you'll be doing basing algebra to solve the problem. It's understandable if your skills are a little rusty, but you have to embrace the challenge and hone those skills, since they're essential on the Quant section.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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