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An optometrist charges $150 per pair for soft contact lenses

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An optometrist charges $150 per pair for soft contact lenses

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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

The OA is B

Source: GMAT Paper Tests

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swerve 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.

The correct answer is B.

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