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

37 small prints and 15 large prints

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.

Answer 2

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

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`