SAT Advanced Percentage and Compound Growth Investment Practice Questions

The amount after five years can be calculated using the formula for compound interest: \(A = P(1 + r)^n\), where \(P = 10,000\), \(r = 0.10\), and \(n = 5\). So, \(A = 10,000(1 + 0.10)^5 = 10,000 \\times 1.61051 = 16,105.10\). The percentage increase is \(frac{16,105.10 - 10,000}{10,000} \\times 100 = 61.051 \\%\).

Initially, the student answered \(0.75 \\times 120 = 90\) questions correctly. To achieve \(85 \\%\), they need to answer \(0.85 \\times 120 = 102\) questions correctly. Therefore, they need \(102 - 90 = 12\) more correct answers.

After three hours, the population is \(P \\times 2^3 = 8P\). If \(30 \\%\) of the population dies, the remaining population is \(70 \\%\) of \(8P\), which is \(0.7 \\times 8P = 5.6P\).

After one year, the car's value is \(20,000 \\times (1 - 0.15) = 20,000 \\times 0.85 = 17,000\). After another year, the value is \(17,000 \\times 0.85 = 14,450\).

Let the original price be \(P\). After a \(20 \\%\) increase, the new price is \(1.2P\). A \(10 \\%\) discount on \(1.2P\) results in \(0.9 \\times 1.2P = 1.08P\). Given that the final price is \(108\), we have \(1.08P = 108\). Solving for \(P\) gives \(P = 100\).

Let \(x\) be the original number. The equation is \( x + 0.25x = 225 \), simplifying to \(1.25x = 225\). Solving for \(x\) gives \(x = 180\).

Calculate using the formula: \( \\frac{150}{100} \\times 180 = 270 \).

Using the equation \( \\frac{z}{100} \\times 700 = 210 \), we solve for \(z\) to get \(z = 30\).

Use the formula: \( \\frac{90}{300} \\times 100 = 30 \\% \).

Let \(x\) be the original number. The equation is \( x - 0.3x = 140 \), simplifying to \(0.7x = 140\). Solving for \(x\) gives \(x = 200\).

Calculate using the formula: \( \\frac{120}{100} \\times 200 = 240 \).

Set up the equation \( \\frac{y}{100} \\times 500 = 150 \). Solving for \(y\) yields \(y = 30\).

Let \(x\) be the original number. The equation is \( x + 0.2x = 240 \), which simplifies to \(1.2x = 240\). Solving for \(x\) gives \(x = 200\).

The value can be found by calculating: \( \\frac{85}{100} \\times 160 = 136 \).

We can set up the equation: \( \\frac{x}{100} \\times 480 = 96 \). Solving for \(x\) gives us \(x = 20\).