(3) If there is a fraction in both members find a common denominator, and multiply both members by it.

Find the value of x in the equation

8/2

2

=

Make a rule for clearing an equation of fractions.

319. SOLUTION OF PROBLEMS INVOLVING FRACTIONAL EQUATIONS.

The sum of two numbers is 320, and the quotient of the greater number divided by the less is 3. What are the num

1. Mr. Reed paid for his carriage § as much as he paid for his horse. The horse cost $64 more than the carriage. What was the cost of each ?

2. Five times Anne's money increased by of her money is equal to $464. How much money has she?

3. The difference between of a man's age and of his age is 4 years. How old is he?

4. Mr. Hudson, Mr. Childs, and Mr. Lewis engaged in business with a capital of $14,000. Mr. Childs putas much money in the business as Mr. Hudson, and Mr. Lewis put in as much as Mr. Childs. What part of the capital did each provide?

5. The weight of a team with a load of coal is 5500 lb. The team weighs as much as the coal, and the wagon weighs as much as the team. What is the weight of each?

6. Harry and his sister Celia have together $.64. Celia has 12 cts. more than Harry. How much have each.

7. Mr. Kennedy sold two plots of land containing 80 acres in all. One. lot is 10 acres larger than the other. What is the size of each plot?

8. In a school of 1,200 pupils the girls outnumbered the boys by 120. How many were there of each?

9. Mr. Harris spent $2 for 5-cent stamps, 2-cent stamps and postal cards. He bought 30 more 2-cent stamps than 5-cent stamps, and 30 more postal cards than 2-cent stamps. How many did he buy of each?

10. The sum of two numbers is 30. Three times the first number added to four times the second is 104.

What are

11. There are

the boys by 15.

865 pupils in a school. The girls exceed What is the number of each?

12. $2,400 is divided among three children. The second receives twice as much as the first, and the third receives five times as much as the first. What is the share of each?

13. 175 is the difference between six times a certain number and eleven times the same number. What is the number?

14. The sum of three numbers is 240. The second is double the first and the third is four times the sum of the other two. What are the numbers?

15. Frank and Edward had together 72 marbles. Edward gave Frank four of his marbles. Frank then had twice as many as Edward. How many marbles had each?

16. The sum of the ages of a father and a son is 68 years. In 6 years the father's age will be three times the age of the What is the age of each?

son.

17. On Saturday, Sept. 14, 1907, Mr. Dalrymple deposited 45 bills in a bank. Some of them were $5 bills and the others $10 bills. The amount deposited was $325. How many of each did he deposit?

18. Mr. Macy sold 4 baskets of apples and 8 baskets of peaches for $13.80, and 8 baskets of apples and 4 baskets of peaches for $9.60. How much did he receive for a basket of apples? Of peaches?

98

19. The ages of Mr. Matthews and his son together make years. Ten years ago Mr. Matthews was twice as old as his son. What is the age of each now?

CHAPTER VII

MENSURATION

PLANE FIGURES

POLYGONS

321. What is a plane figure? Name five plane figures. A plane figure bounded by straight lines is called a polygon. Squares, triangles, hexagons, are examples of polygons.

A polygon is named from the number of its sides or angles.

How many sides has a triangle? A quadrangle? A pentagon? A hexagon? An octagon? How many angles has each figure named?

In previous lessons, the following rules for finding the areas of plane figures have been learned:

1. The area of a triangle is equal to the product of the base by the altitude. 2. The area of a rectangle is equal to the product of the length by the breadth.

3. The area of a parallelogram is equal to the product of the base by the altitude.