Ella is a landscape photographer . One weekend at her gallery she sells a total of 52 prints for a total of $ 2,975. How many of each size print did Ella sell?

The correct answer is: Ella sold 37 small prints and 15 large prints

Complete step by step solution:
Let the number of small prints = x
And the number of large prints = y
Total number of prints sold = 52
⇒x + y = 52…(i)
Price of one small print =
And Price of one large print =
Total money she earns =
⇒50x + 75y=2975…(ii)
On multiplying (i) with 50, we get 50(x + y = 52)
⇒ 50x + 50y = 2600…(iii)
Now, we have the coefficients of x in (ii) and (iii) to be the same.
On subtracting (iii) from (ii),
we get LHS to be 50x + 75y - (50x + 50y) = 75y - 50y = 25y
and RHS to be 2975 - 2600 = 375
On equating LHS and RHS, we have 25y = 375
⇒y = 15
On substituting the value of  in (i), we get x + 15 = 52
⇒ x = 52 - 15
⇒ x = 37
Hence we get = 37 and y = 15
Ella sold 37 small prints and 15 large prints.
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.