Question

Ella is a landscape photographer. One weekend at her gallery she sells a total of 52 prints for a total of $2,975. A small painting cost $50 and a large painting cost $75. How many of each size print did Ella sell?

Answer 1

Answer:37 paintings of $50 and 15 paintings of $75

Step-by-step explanation:

Let $x$ be the number of paintings Ella sells for $$50$.

Let $y$ be the number of paintings Ella sells for $$75$.

Profit made through $$50$ paintings is $50x$

Profit made through $$75$ paintings is $75y$

So,total profit is given by $50x+75y$

It is given that total profit is $$2975$

So,$50x+75y=2975$      ..(i)

Given that the total number of prints is $52$

So,$x+y=52$      ..(ii)

using (i) and (ii),

$50x+75(52-x)=2975\\50x+3900-75x=2975\\25x=925\\x=37$

$y=52-x=52-37=15$

Answer 2

Answer:

37 small prints and 15 large prints

Step-by-step explanation:

       Ella sold a total of 52 prints for a total of $ 2,975. Small prints cost $ 50 and large prints cost $ 75.

       Let us denote the number of small prints sold by $x$ and the number of large prints sold by $y$.

       Total number of prints sold = $x+y=52$        -$(i)$

       Total amount = $50x+75y=2975$                        -$(ii)$

Multiplying first equation with 50 and subtacting it from second equation,

       $50x+75y-50x-50y=2975-50(52)\\25y=375\\y=15\\x=37$

∴ Ella sold 37 small prints and 15 large prints.