Question

problem statement
a smartphone accessory kiosk is analyzing its daily sales of two popular items: tempered glass screen protectors and rugged phone cases.
the owner notices a pattern in how these items sell and tracks the total revenue:

1. the inventory pattern: customers often buy cases for their friends, but screen protectors are an add - on. the number of phone cases sold (y) was 4 fewer than 3 times the number of screen protectors sold (x).
2. the revenue rule: screen protectors cost $10 each, and phone cases cost $25 each. the total revenue generated from these two items today was $1,600.

how many of each item were sold?

Explanation:

Step1: Define variables and form equations

Let \( x \) be the number of Screen Protectors sold and \( y \) be the number of Phone Cases sold. From the inventory pattern: \( y = 3x - 4 \). From the revenue rule: \( 10x + 25y = 1600 \).

Step2: Substitute \( y \) into revenue equation

Substitute \( y = 3x - 4 \) into \( 10x + 25y = 1600 \):
\( 10x + 25(3x - 4) = 1600 \)
Expand: \( 10x + 75x - 100 = 1600 \)
Combine like terms: \( 85x - 100 = 1600 \)

Step3: Solve for \( x \)

Add 100 to both sides: \( 85x = 1700 \)
Divide by 85: \( x = \frac{1700}{85} = 20 \)

Step4: Solve for \( y \)

Substitute \( x = 20 \) into \( y = 3x - 4 \):
\( y = 3(20) - 4 = 60 - 4 = 56 \)

Answer:

Screen Protectors sold: \( \boldsymbol{20} \), Phone Cases sold: \( \boldsymbol{56} \)