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505-555 (Easy)|   Word Problems|            
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ajit257
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An optometrist charges $150 per pair for soft contact lenses and $85 25 Dec 2010, 08:00
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B
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15% (low)

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87% (02:29) correct 13% (02:54) wrong based on 802 sessions

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An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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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B
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An optometrist charges $150 per pair for soft contact lenses and $85 25 Dec 2010, 08:24
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Let the number of sold pairs of hard lenses be X, then the number of sold soft lenses is x+5. x+x+5=?

(x+5)*150 + x*85 =1690
235*x=940
x=4
2*x+5=13

Maybe you have forgotten to add the number of sold lenses of the other type.
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An optometrist charges $150 per pair for soft contact lenses and $85 25 Dec 2010, 09:18
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ajit257
An optometrist charges $150 per pair for soft contact
lenses and $85 per pair for hard contact lenses. Last
week she 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

Not sure about the way i solved it.
Show more

(x+5)*150 +x*85=1690
=>x=4

total lens=4+(4+5)= 13
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An optometrist charges $150 per pair for soft contact lenses and $85 26 Sep 2016, 23:19
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s = h +5 ; 150(s) + 85(h) = 1690

15(h+5)+85(h) = 1690 => h =4 anf s => 4+5 = 9

h +s = 13
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An optometrist charges $150 per pair for soft contact lenses and $85 18 Oct 2016, 11:31
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Let x = soft lenses
y = hard lenses

x = y+5

150x +85y = 1690
150(y+5)+85y = 1690 --> y = 4 --> x = 9

4+9=13 (total lenses)
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An optometrist charges $150 per pair for soft contact lenses and $85 28 Mar 2019, 13:46
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ajit257
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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
Show more

Since $150 soft lenses and $85 hard lenses yield $1690 in revenue, we get:
150S + 85H = 1690
30S + 17H = 238

The sum on the left side must yield a units digit of 8.
Since 17*4 = 68, it is likely that H=4:
30S + 17*4 = 338
30S + 68 = 238
30S = 170
S=9

S=9 and H=4 satisfy the condition that the optometrist sells 5 more pairs of soft lenses than hard lenses.
Thus, the total number of pairs = 9+4 = 13.

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B
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An optometrist charges $150 per pair for soft contact lenses and $85 31 Mar 2019, 11:53
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ajit257
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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
Show more

We can let n = the number of pairs of soft contact lenses and m = the number of pairs of hard contact lenses and create the equations

n = m + 5

and

150n + 85m = 1690

30n + 17m = 338

Substituting, we have:

30(m + 5) + 17m = 338

30m + 150 + 17m = 338

47m = 188

m = 4

So n = 9, and the total number of pairs of lenses she sold is 9 + 4 = 13.

Answer: B
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An optometrist charges $150 per pair for soft contact lenses and $85 26 Jun 2021, 08:32
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Let the number of pairs of soft contact lenses be S and the number of pairs of hard contact lenses be H.

Charges for 1 pair of soft contact lenses = $150
Charges for 1 pair of hard contact lenses = $85

The optometrist sold 5 more pairs of ‘Soft’ than ‘Hard; therefore, S = H + 5.
Her total sales for last week was $1690; therefore, 150 * S + 85 * H = 1690.

Substituting the value of S = H + 5 in the equation, we have,
150 ( H + 5) + 85 H = 1690.
150 H + 750 + 85 H = 1690
235 H = 1690 – 750
235 H = 940.
Simplifying, we obtain H = 4 and therefore, S = 4 + 5 = 9.
Total number of pairs of contact lenses sold = H + S = 4 + 9 = 13.

The correct answer option is B.

Hope that helps!
Aravind BT
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An optometrist charges $150 per pair for soft contact lenses and $85 22 May 2023, 00:44
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ajit257
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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

Since $150 soft lenses and $85 hard lenses yield $1690 in revenue, we get:
150S + 85H = 1690
30S + 17H = 238

The sum on the left side must yield a units digit of 8.
Since 17*4 = 68, it is likely that H=4:
30S + 17*4 = 338
30S + 68 = 238
30S = 170
S=9

S=9 and H=4 satisfy the condition that the optometrist sells 5 more pairs of soft lenses than hard lenses.
Thus, the total number of pairs = 9+4 = 13.

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B
.
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I think it should be 30S = 270; S = 9; You made a typo there. :)
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An optometrist charges $150 per pair for soft contact lenses and $85 22 May 2023, 08:13
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ajit257
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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
Show more
\(150(h+5) + 85h = 1690\)

\(150h + 750 + 85h = 1690\)

\(235h = 940\)

Thus, h = 4 and s = 4 + 5 => 9

Hence, total no of pairs of contact lenses that she sold is 9 + 4 = 13, Answer must be (B)
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An optometrist charges $150 per pair for soft contact lenses and $85 22 May 2023, 08:23
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ajit257
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she 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
\(150(h+5) + 85h = 1690\)

\(150h + 750 + 85h = 1690\)

\(235h = 940\)

Thus, h = 4 and s = 4 + 5 => 9

Hence, total no of pairs of contact lenses that she sold is 9 + 4 = 13, Answer must be (B)
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yea, that's how I did it as well but GmatGuruNY used an interesting trick there to solve this. Although, I don't think it's very realistic, I mean, you can't possibly say that it "MUST" be 4, I mean, 17*14 will also have an 8 in the end so it's not exactly a trick you can use everytime but still, it's interesting and a trick worth knowing. :)
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An optometrist charges $150 per pair for soft contact lenses and $85 06 Jul 2024, 08:14
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friends, any tips for the math part here? I find it takes time and then i start stressing.
I also simplified and it still takes time; in such questions where the maths takes time, how do i make the decision between let me just do the math and "there must be an easier way"?­
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An optometrist charges $150 per pair for soft contact lenses and $85 08 Sep 2025, 13:59
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