From your assumed total, compute how many model X and model Y gadgets you had before retooling, then apply the given percent increase and decrease to those counts.

Once you have the new counts of model X and Y, use the fact that the total number of gadgets is unchanged to find what fraction of the new total is model X, then convert that fraction to a percent.

In Desmos, type 30*1.7 (for the 70% increase of model X from 30 gadgets) and 70*0.7 (for the 30% decrease of model Y from 70 gadgets). Note the two results as the new counts for models X and Y.

In Desmos, type 30*1.7 + 70*0.7 to verify that the total number of gadgets is unchanged. Then type 30*1.7 / (30*1.7 + 70*0.7) to get the new fraction of gadgets that are model X. Read the decimal output and convert it to a percentage to match one of the answer choices.

Because only percentages and relative changes matter, you can assume any total number of gadgets. Use 100 gadgets to keep the arithmetic simple.

• Before retooling:
  • Model X: $30\%$ of $100 = 30$ gadgets
  • Model Y: $70\%$ of $100 = 70$ gadgets

So we start with 30 model X and 70 model Y gadgets.

Now change each model’s count according to the problem:

• Model X increases by $70\%$:

  • Increase amount: $70\%$ of $30 = 0.70 \times 30 = 21$
  • New model X count: $30 + 21 = 51$

• Model Y decreases by $30\%$:

  • Decrease amount: $30\%$ of $70 = 0.30 \times 70 = 21$
  • New model Y count: $70 - 21 = 49$

After retooling, there are 51 model X gadgets and 49 model Y gadgets.

Check the total after retooling:

• New total gadgets: $51 + 49 = 100$, which matches the original total, as stated in the problem.

Now find the new percentage of model X gadgets:

• Fraction that is model X: $\dfrac{51}{100}$
• As a percent, this is 51%, so the correct answer is 51% (choice C).