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An optometrist charges $150 per pair for soft contact lenses and $85

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An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 25 Dec 2010, 08:00
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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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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 25 Dec 2010, 08:24
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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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 25 Dec 2010, 09:18
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ajit257 wrote:
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.


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

total lens=4+(4+5)= 13
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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 26 Sep 2016, 23:19
2
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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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 18 Oct 2016, 11:31
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1
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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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 28 Mar 2019, 13:46
ajit257 wrote:
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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Re: An optometrist charges $150 per pair for soft contact lenses and $85  [#permalink]

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New post 31 Mar 2019, 11:53
ajit257 wrote:
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


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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Re: An optometrist charges $150 per pair for soft contact lenses and $85   [#permalink] 31 Mar 2019, 11:53
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