Question

A photographer sells large photos for $27 profit and small photos for an $11 profit.This past year,she sold 126 photos and made a profit of $2,250.How many of each size photo did she sell?

Answer 1

She sold 72 small photos and 54 large photos.

Explanation:

We can set a equations system with the given information. Let X be the quantity of small photos and Z large photos.

We are told that she sold 126 photos in total, so:

X + Z = 126

Also, she earned 2,250 by selling certain quantities of small photo and large photos, so:

$2,250 = $11X + $27Z

From the first equation we get that X=126-Z, replace that into the 2nd equation:

2,250 = 11(126-Z) +27Z

2,250 = 1,386 - 11Z + 27Z

2,250 - 1,386 = 16Z

864 = 16Z

Z = 864/16

Z = 54 is the number of large photos sold. Now find X.

X = 126 - Z

X = 126 - 54

X = 72 is the number of small photos sold.