A $30\%$ loss is not $x - 30$; it is $x$ multiplied by a number less than $1$. What number do you multiply by for a $30\%$ loss? What about a $50\%$ gain and a $20\%$ loss?

After applying all three multipliers in order to $x$, you should get $70{,}560$. Write an equation of the form (multiplier)$\times x = 70{,}560$, then solve for $x$.

In a new expression line, type 0.7*1.5*0.8 to confirm the overall multiplier relating the starting value to the final value.

In another expression line, type 70560/(0.7*1.5*0.8). The numerical result that Desmos shows is the original value of the portfolio at the beginning of 2019.

A percent loss means multiply by $(1 - \text{percent})$, and a percent gain means multiply by $(1 + \text{percent})$.

• Losing $30\%$ means multiply by $1 - 0.30 = 0.7$.
• Gaining $50\%$ means multiply by $1 + 0.50 = 1.5$.
• Losing $20\%$ means multiply by $1 - 0.20 = 0.8$.

So the value is multiplied in sequence by $0.7$, then $1.5$, then $0.8$.

Let $x$ be the value of the portfolio at the beginning of 2019.

After each change:

• After the $30\%$ loss: value is $0.7x$.
• After the $50\%$ gain: value is $0.7x \cdot 1.5$.
• After the $20\%$ loss: value is $0.7x \cdot 1.5 \cdot 0.8$.

We are told this final amount is $70{,}560$, so:

Now multiply the decimals:

So the equation becomes $0.84x = 70{,}560$.

From the simplified equation

divide both sides by $0.84$ to isolate $x$:

Now you just need to compute this division.

To compute $x = \dfrac{70{,}560}{0.84}$, you can clear the decimal by multiplying top and bottom by $100$:

Now divide:

So the portfolio was worth $84{,}000$ at the beginning of 2019, which corresponds to choice D) 84,000.