Question

1. 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?

small: $50
large: $75

Explanation:

Step1: Define Variables

Let \( x \) be the number of small prints and \( y \) be the number of large prints. We know two equations:

1. \( x + y = 52 \) (total number of prints)
2. \( 50x + 75y = 2975 \) (total revenue)

Step2: Solve the System of Equations

From the first equation, we can express \( x \) as \( x = 52 - y \). Substitute this into the second equation:

$$ 50(52 - y) + 75y = 2975 $$

$$ 2600 - 50y + 75y = 2975 $$

$$ 25y = 2975 - 2600 $$

$$ 25y = 375 $$

$$ y = \frac{375}{25} = 15 $$

Then substitute \( y = 15 \) back into \( x = 52 - y \):

$$ x = 52 - 15 = 37 $$

Answer:

Small prints: 37, Large prints: 15