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by BlueDragon2010 » Sat Dec 21, 2013 3:36 pm
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week sh sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

A) 11

B) 13

C) 15

D) 17

E) 19
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by Brent@GMATPrepNow » Sat Dec 21, 2013 3:54 pm
BlueDragon2010 wrote:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week sh sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

A) 11
B) 13
C) 15
D) 17
E) 19
We can solve this question using two variables or one variable.

First ONE variable.

Last week she sold 5 more pairs of soft lenses than hard lenses.
Let H = # of pairs of hard lenses sold.
So H + 5 = # of pairs of soft lenses sold.

Optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Total sales for pairs of contact lenses last week were $1,690
150(H + 5) + 85H = 1690 SOLVE

Expand: 150H + 750 + 85H = 1690
Simplify: 235H = 940
H = 4

So, 4 pairs of hard lenses were sold, which means 9 pairs of soft lenses were sold.
TOTAL pairs sold = 4 + 9 = [spoiler]13 = B[/spoiler]

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Dec 21, 2013 4:06 pm
BlueDragon2010 wrote:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week sh sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

A) 11
B) 13
C) 15
D) 17
E) 19
Now, TWO variables.

Let H = # of pairs of hard lenses sold.
Let S = # of pairs of soft lenses sold.

Last week she sold 5 more pairs of soft lenses than hard lenses.
So, S - H = 5

Optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Total sales for pairs of contact lenses last week were $1,690
150S + 85H = 1690

We now have two equations:
S - H = 5
150S + 85H = 1690

Divide bottom equation by 5 to get:
S - H = 5
30S + 17H = 338

By the way, we have a free video showing a quick way to divide by 5 in your head: https://www.gmatprepnow.com/module/gener ... es?id=1112

Multiply top equation by 17 to get:
17S - 17H = 85
30S + 17H = 338

Add equations to get: 47S = 423
So, S = 9
If S = 9, then H = 4

TOTAL pairs sold = 4 + 9 = [spoiler]13 = B[/spoiler]

Cheers,
Brent
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by Patrick_GMATFix » Sat Dec 21, 2013 4:27 pm
The solution below is taken from the GMATFix App.

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by GMATGuruNY » Sat Dec 21, 2013 5:07 pm
BlueDragon2010 wrote:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week sh sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

A) 11

B) 13

C) 15

D) 17

E) 19
The total amount of revenue -- $1690 -- is a multiple of 10.
Since the price of each pair of soft lenses is a multiple of 10, the total amount of revenue from the soft lenses must be a multiple of 10.
Implication:
The total amount of revenue from the hard lenses must also be a multiple of 10.
Since the price of each pair of hard lenses is $85, the number of pairs of hard lenses sold must be an EVEN integer.

Case 1: 2 pairs of hard lenses sold
Since 5 more pairs of soft lenses are sold, the number of pairs of soft lenses sold = 2+5 = 7.
Total pairs sold = 2+5 = 7.
Since 7 is not among the answer choices, Case 1 is not viable.

Case 2: 4 pairs of hard lenses sold
Since 5 more pairs of soft lenses are sold, the number of pairs of soft lenses sold = 4+5 = 9.
Total pairs sold = 4+9 = 13.
This is the value in answer choice B.
Check whether Case 2 yields $1690 in revenue:
(4*85) + (9*150) = 340 + 1350 = 1690.
Success!

The correct answer is B.
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