7 Tara is saving for an overseas trip. Her taxable income is usually about $$ \$ 20000 $$. She estimates that she will need $$ \$ 5000 $$ for the trip, so she is going to do some extra work to raise the money. How much extra will she need to earn in order to have an extra $$ \$ 5000 $$ after tax?

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Tara wants an extra amount of \$5000 after paying tax. Because the taxes are applied on her additional earnings, she must earn extra so that after the tax is taken out she has \$5000 left. Her taxable income is normally about \$20000, which means any extra dollars she earns will be taxed at her marginal tax rate. In her case, the extra income falls in the same tax bracket. For a taxpayer with taxable income near \$20000, the marginal tax rate is typically 15%.

Let the extra (gross) earnings she must work for be $$x$$. Since 15% of $$x$$ is taken as tax, she retains $$85\%$$ of $$x$$, or
$$
0.85x.
$$
She wants this amount to equal \$5000:
$$
0.85x = 5000.
$$
To solve for $$x$$, divide both sides of the equation by 0.85:
$$
x = \frac{5000}{0.85}.
$$
Calculating, we get:
$$
x \approx 5882.35.
$$
Thus, Tara needs to earn approximately \$5882 extra in order to have \$5000 after tax.
Tara needs to earn approximately \$5882 extra to have \$5000 after taxes.

7 Tara is saving for an overseas trip. Her taxable income is usually about \( \$ 20000 \). She estimates that she will need \( \$ 5000 \) for the trip, so she is going to do some extra work to raise the money. How much extra will she need to earn in order to have an extra \( \$ 5000 \) after tax?

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