Question

Alexis and Trinity run two stores. On the first day Alexis puts everything on sale in her store by 25.0% while Trinity marks down all prices in her store by 20%. On the second day Alexis takes an additional 1/3 off all her prices. By what fraction must Trinity mark down all prices in her store, so that the overall price decreases in both stores are the same?

1. kimchi2
The fraction that Trinity must mark down all prices in her store so that the overall price decreases in both stores are the same is 3/8, 0.375, or 37.5%

What is a markdown?

A markdown is a price reduction strategy used by retailers to attract customers to their stores.
A markdown reduces the profit margin.

Alexis:

First day’s price reduction = 25%
Reduced price after the first markdown = 75% (1 – 25%)
The second day’s price reduction = 1/3 or 33.33%
Reduced price after the second markdown = 50% (75% x (1 – 33.33%)

Trinity:

First day’s price reduction = 20%
Reduced price after the first markdown = 80% (1 – 20%)
Reduced price after the second markdown = 50% like Alexis’ (80% x 50%/80%)
50%/80% = 62.5% or 0.625
Therefore, the second day’s price reduction must be 3/8, 0.375, or 37.5% (1 – 0.625).
Thus, the fraction that Trinity must mark down all prices in her store so that the overall price decreases in both stores are the same is 3/8