Question 23·Medium·Percentages
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?
For percent-increase problems, first convert the percent change into a multiplier (for example, a increase becomes a factor of ) and apply it to get the new total. Then apply any given percentage (here, the whole-wheat) to the updated total, not the original. When multiple percentages are applied in sequence to the same starting amount, you can often multiply all the factors in one line (like original total ) to save time and reduce errors.
Hints
Interpret the 25% increase
When a quantity is increased by , how can you represent the new amount as a single multiplication factor (for example, something)?
Work with the new total, not the old one
First find how many total loaves the bakery plans to make next week after the increase. Only then should you apply the for whole-wheat loaves.
Apply the 12% to the correct quantity
Once you know next week's total number of loaves, how do you find of that number? You can multiply by or by .
Desmos Guide
Compute the final number directly
In Desmos, type 8400*1.25*0.12 (or 8400*1.25*(12/100)) and look at the numeric result of the expression; that value is the number of whole-wheat loaves planned for next week.
Step-by-step Explanation
Find next week's total number of loaves
"Increase by " means multiply the original amount by .
So next week the bakery plans to produce loaves in total.
Use the same percentage of whole-wheat loaves
The bakery will keep of its loaves as whole-wheat. To find of the new total, multiply the new total by (or ):
This calculation gives the number of whole-wheat loaves planned for next week.
Compute the number of whole-wheat loaves
Now calculate:
So, the bakery plans to bake 1,260 whole-wheat loaves next week.