In 2018 a factory produced widgets at a constant rate of widgets per week. By 2020, the weekly production rate had risen to widgets per week, and the factory still operated the same weeks each year.
By how many widgets did the factory’s total yearly production increase from 2018 to 2020?
For rate-and-time questions where two scenarios use the same time period (like the same number of weeks), avoid doing two full calculations. Instead, first subtract the rates to get the difference per unit time, then multiply that difference by the common time period. Break multiplications into easy parts (for example, use ) to do them quickly and accurately without a calculator.
Hints
Connect weekly and yearly production
How do you turn a weekly production rate into a yearly total if the factory works all weeks?
Use the fact that both years have 52 weeks
Since both years use the same weeks, you don’t have to compute both yearly totals separately. What happens if you first find how many more widgets are made each week in 2020 than in 2018?
Scale the weekly increase
Once you know the extra number of widgets per week, multiply that number by to find the extra widgets per year.
Check your arithmetic
Be careful with subtraction and the multiplication by . You can break into to make the multiplication easier.
Desmos Guide
Compute the yearly increase directly
In Desmos, type the expression (28500 - 23000)*52 and look at the numerical result. That value is the increase in the factory’s total yearly production from 2018 to 2020.
Step-by-step Explanation
Identify what the question is asking
The question asks for how many more widgets per year the factory produced in 2020 compared to 2018.
Each year’s total production is:
- (weekly production rate) × (number of weeks in a year).
Since the factory works weeks in both years, you can either:
- find each year’s total and then subtract, or
- find the difference in weekly rates and then multiply by 52.
The second way is faster.
Find the increase in weekly production
Compute how many more widgets per week the factory produced in 2020 than in 2018:
So the weekly production increased by widgets per week.
Convert the weekly increase to a yearly increase
Now multiply the extra widgets per week by the weeks in a year:
Break it into easier pieces:
Add these partial products:
State the final answer and match to the choices
The factory’s total yearly production increased by 286,000 widgets from 2018 to 2020.
This corresponds to choice C) 286,000.