A change to one group followed by a question about its share of the total combines percent change with a part-whole percent. When only percentages are given, choose an original total of and find the starting size of the group that changes. Apply the increase to that group, then compare its new size with the new total. The increase is not taken from the whole factory output.
Hints
- Hint 1
With no starting total specified, you can choose a starting total of gadgets. Percent shares stay the same when every count is scaled together. How many of those would originally be model X?
- Hint 2
A percent increase adds to the original amount rather than replacing it. Model X keeps all of its starting count and gains another of that count. What percent of its original count does it have afterward?
- Hint 3
A part-whole percent compares the new model X count with the new total, not with the original model X count. The factory's total stays at the number you chose. What does the new X count mean out of ?
Step-by-step
Choose a total of 100
Step 1Find the starting model X count
Choose as a convenient original total, since the problem gives percentages but no gadget counts. Type in Desmos. It returns , so your scaled factory originally makes model X gadgets.
- Step 2
Turn the increase into a new percent
The model X count increases by of its own starting count. It keeps the original and gains another . Add those shares to get its new amount as a percent of its old amount:
Don't take the increase from all gadgets; it applies to model X.
- Step 3
Find the new share of all gadgets
Type on the next Desmos line. It returns , the new model X count. The total remained , so compare the new X count with that total:
After retooling, of the gadgets were model X. Choice C.