Loading...
A retail store has 60 employees—full-time salespeople (FT sales), part-time salespeople (PT sales), and managers—in the proportions shown by the graph. Each full-time salesperson and each manager works the same number of hours per week; each part-time salesperson works exactly half that many hours per week.
The store wants the ratio of the total number of hours worked per week by full-time salespeople to the total number of hours worked by part-time salespeople to be 2:3 and wants to achieve this ratio without changing the number of managers or the number of hours each manager works per week.
Based on the information provided, select the option from each drop-down menu that creates the most accurate statement.
| Text Component | Literal Content | Simple Interpretation |
|---|---|---|
| Total workforce | "A retail store has 60 employees" | The store employs exactly 60 people |
| Employee categories | "full-time salespeople (FT sales), part-time salespeople (PT sales), and managers" | There are three types of employees: FT salespeople, PT salespeople, and managers |
| Proportions reference | "in the proportions shown by the graph" | Employee category sizes are detailed in the accompanying chart |
| Work hours | "Each full-time salesperson and each manager works the same number of hours per week; each part-time salesperson works exactly half that many hours per week." | FT sales and managers work the same weekly hours; PT sales work half as much |
| Desired work hours ratio | "The store wants the ratio of the total number of hours worked per week by full-time salespeople to the total number of hours worked by part-time salespeople to be 2:3" | The goal is for FT total hours : PT total hours = \(\mathrm{2:3}\) |
| Managers constraint | "without changing the number of managers or the number of hours each manager works per week" | The number of managers and their hours must remain constant |
| Chart Component | What's Shown | What This Tells Us |
|---|---|---|
| Chart type | Pie chart, single with three slices | Depicts employee distribution by category |
| PT sales slice | 60% of pie | PT salespeople make up 60% of employees (36 out of 60) |
| FT sales slice | 30% of pie | FT salespeople are 30% of employees (18 out of 60) |
| Managers slice | 10% of pie | Managers represent 10% of employees (6 out of 60) |
| Relative sizes | PT : FT : Managers = 60 : 30 : 10 | Most employees are PT, then FT, then managers |
| Key proportions | PT is twice FT, both are much larger than managers | PT salespeople dominate the workforce |
To achieve the desired ratio, the store could [BLANK 1] the number of full-time salespeople
and [BLANK 2] the number of part-time salespeople
To achieve the required \(\mathrm{2:3}\) full-time to part-time sales hours ratio, the store should decrease the number of full-time salespeople by 4 (from 18 to 14) and increase the number of part-time salespeople by 6 (from 36 to 42), while keeping the total number of non-manager employees constant.
The two blanks are dependent on each other. The changes to full-time and part-time salespeople must work together to maintain the total number of non-manager employees and achieve the target \(\mathrm{2:3}\) ratio; the answer to one blank determines the answer to the other.