Last week, a bakery produced 8,400 loaves of bread, and 12% of them were whole-wheat loaves. For the coming week, the bakery plans to increase its total production by 25% while keeping the same percentage of whole-wheat loaves. How many whole-wheat loaves does the bakery plan to bake next week?
A percent increase changes the total, while a fixed category percentage tells you what share of that total belongs to one group. First add the increase to the original and use Desmos to find the new total. Then take the category percentage of that new total. Using the old total gives last week’s group count instead.
Hints
- Hint 1
An increase adds to what was already there. Start with of last week’s production and add the increase. What percent of last week’s total does that make next week’s total?
- Hint 2
The base of a percent is the amount it’s taken of. The whole-wheat percentage stays at , but next week it’s taken of next week’s total, not last week’s.
Step-by-step
Find the new total, then its whole-wheat share
Step 1Turn the increase into a percent of last week’s total
A percent increase keeps the original and adds the extra . Add those shares: . So next week’s total is of loaves. The extra alone isn’t the new total.
- Step 2
Calculate next week’s total
Type in Desmos. It shows , so the bakery plans to make loaves in all next week.
- Step 3
Use the new total as the percent base
The whole-wheat percentage stays at , but its base, the total it’s taken of, has changed. Take the fixed percentage of the new total. So the planned whole-wheat count is of , not of .
- Step 4
Calculate the whole-wheat count
Add in Desmos. It shows , so the bakery plans to bake whole-wheat loaves next week. Choice B.