Part 5

3. Solve [2(x - 7)]/(x^2 + 3x - 28) + (2 - x)/(4 - x) - (x + 3)/(x + 7) = 0.

_Group II_

4. Simplify [2^(1/2) + 2[3^(1/2)]]/[2^(1/2) - 12^(1/2)], and compute the value of the fraction to two decimal places.

5. Solve the simultaneous equations { x^(-1/2) + 2y^(-1/2) = 7/6, { 2x^(-1/2) - y^(-1/2) = 2/3.

_Group III_

6. Two numbers are in the ratio of c : d. If a be added to the first and subtracted from the second, the results will be in the ratio of 3 : 2. Find the numbers.

7. A dealer has two kinds of coffee, worth 30 and 40 cents per pound. How many pounds of each must be taken to make a mixture of 70 pounds, worth 36 cents per pound?

8. A, B, and C can do a piece of work in 30 hours. A can do half as much again as B, and B two thirds as much again as C. How long would each require to do the work alone?

~YALE UNIVERSITY~

ALGEBRA B

TIME: ONE HOUR

Omit one question in Group I and one in Group II. Credit will be given for _five_ questions only.

_Group I_

1. Solve (x + a)/(x + b) + (x + b)/(x + a) = 5/2.

2. Solve the simultaneous equations { x^2y^2 + 28xy - 480 = 0, { 2x + y = 11. Arrange the roots in corresponding pairs.

3. Solve 3x^(-3/2) + 20x^(-3/4) = 32.

_Group II_

4. In going 7500 yd. a front wheel of a wagon makes 1000 more revolutions than a rear one. If the wheels were each 1 yd. greater in circumference, a front wheel would make 625 more revolutions than a rear one. Find the circumference of each.

5. Two cars of equal speed leave A and B, 20 mi. apart, at different times. Just as the cars pass each other an accident reduces the power and their speed is decreased 10 mi. per hour. One car makes the journey from A to B in 56 min., and the other from B to A in 72 min. What is their common speed?

_Group III_

6. Write in the simplest form the last three terms of the expansion of (4a^(3/2) - a^(1/2) x^(1/3))^8.

7. (_a_) Derive the formula for the sum of an A. P.

(_b_) Find the sum to infinity of the series 1, -1/2, 1/4, -1/8, ···. Also find the sum of the positive terms.

End of Project Gutenberg's A Review of Algebra, by Romeyn Henry Rivenburg