Question

1. solve the proportion below. (4pts)\\(\frac{12}{x + 5}=\frac{2}{3}\\)\\(\frac{12\cdot3}{x + 5}=\frac{2\cdot3}{3}\\)\\(12\cdot3 = 2(x + 5)\\)\\(36 = 2x + 10\\)\\(36 - 10 = 2x\\)\\(26 = 2x\\)\\(x = 13\\)\\(\\)\\(15) what percent of 90 is 40? show your work using the percent proportion. (3 points)\\(\\)\\(16) jay’lin bought a pair of j’s on sale at a discount of 20%. if the original price of the shoes...\\(a) what is the price of the shoes after the discount is applied? (3 points)\\(\\)\\(b) tax in jay’lin’s state is 6.2%. what is the final price of the shoes, including tax? (3 points)

Explanation:

Step1: Define the percent proportion

The percent proportion is \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\). Here, the part is \(40\), the whole is \(90\), and we let the percent be \(x\). So we set up the equation \(\frac{40}{90}=\frac{x}{100}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives us \(90x = 40\times100\). So \(90x=4000\). Then, to solve for \(x\), we divide both sides of the equation by \(90\): \(x=\frac{4000}{90}=\frac{400}{9}\approx44.44\).

Answer:

\(\frac{400}{9}\%\) or approximately \(44.44\%\)