91Ó°ÊÓ

In each of the following exercises, perform the indicated operations. Express your answer as a single fraction reduced to lowest terms. $$\frac{3 x+7}{4 x}-\frac{x+7}{4 x}$$

In Exercises \(25-60\) solve the problem by first setting up a proportion or an equation. Round off your answers to the nearest hundredth. A currency exchange in Tokyo converts \(\$ 15\) U.S. into 1625.1 Japanese yen. Find the yen value of \(\$ 200\) U.S.

Reduce each of the following rational expressions to lowest terms. $$\frac{5 a-2 x}{15 a-8 x}$$

Solve the equations and inequalities. $$0.6(x-4)-0.4(x-5)=4.6$$

In Exercises \(25-60\) solve the problem by first setting up a proportion or an equation. Round off your answers to the nearest hundredth. A common method for estimating an animal population that is difficult to count is to capture, tag, and then release a certain number of animals. After allowing time for the tagged animals to mix with the untagged, a second group of animals is captured. If we assume that the ratio of tagged to untagged animals is the same for the whole population as it is for the second group, we can set up a proportion to estimate the total population. If 48 deer are captured from a certain area and tagged, and a sample of 60 deer taken after mixing shows 18 are tagged, how many deer are estimated to be in the entire area?

Solve each of the following problems algebraically. Be sure to label what the variable represents. A collection of nickels and dimes is worth \(\$ 1.30 .\) If there are 5 fewer dimes than nickels, how many of each are there?

Solve the equations and inequalities. $$0.035 x+0.052(x+5,000)=1,130$$

Perform the indicated operations. Final answers should be reduced to lowest terms. $$\frac{4 a b+6 a b}{b^{2} \cdot b^{2}} \cdot \frac{2 a^{2} \cdot a^{2}}{4 a^{2} b^{2}+a^{2} b^{2}}$$

Solve the equations and inequalities. $$0.155 x+0.075(80-x)=8.4$$

In each of the following exercises, perform the indicated operations. Express your answer as a single fraction reduced to lowest terms. $$\frac{2}{5 x y}+\frac{1}{10 x^{2}}$$