Algebra

1. Five times a certain number equals 4 more than three times the number?

What is the number?

5x=3x+4

=

+4

It is necessary to have the x's alone for the first member of the equation, and a number alone for the second member. What must be done with both members of the equation to cause the term 3 x to disappear from the second member?

12. Three dollars more than four times my money would be nineteen dollars. How much money have I?

13. Twice a number is 14 more than the number. What is the number?

14. Five times a number less twice the number would be 45. Find the number.

15. Ten marbles less than 5 times the number which Chester has would be 50 marbles. How many has he?

16. The length of a hall is 10 feet less than twice its width. The sum of the length and width is 110 feet. How wide is it?

17. Eight times the circumference of a certain circle would be 42 feet more than five times its circumference. Find the circumference.

First change the equation so as to remove the 3 x from the second member, and then again so as to remove the 7 from the first member. Or transfer both in one step and change the signs of the terms transferred.

-

- 2 x =

10 15. To add 10 and

This, when changed, becomes x then subtract 15 is the same as to subtract 5. So to add x and subtract 2 x is the same as to subtract x. The equation becomes - x=- 5. If to subtract x is the same as to subtract 5, then x 5.

13. If 3 is taken from six times a certain number, the remainder will be 9 more than twice the number.

is the number?

What

14. If 4 is added to twice a number, the result will be 10 less than nine times the number. What is the number? 15. Eight times the money which I have and $9 more would be $65. How much have I?

16. Five times as much money as I have, less $20, would be three times as much as I have. How much have I?

17. In two schoolrooms there are 65 children. In one there are 13 more than in the other. How many are there in each room?

18. A father's age is twice his son's age. The father's age decreased by 13 years would equal the son's age increased by 9 years. How old is each?

Problems for Arithmetic or Algebra

1. A binder bound for me a certain number of histories, 3 times as many novels, and 4 times as many books on science. In all he bound up 24 volumes. How many

of each kind did he bind?

2. A farmer has a certain number of geese, twice as many turkeys, and three times as many chickens. In all he has 72. How many of each has he?

3. I have 3 times as many 5-cent pieces as dimes, and 4 times as many cents as dimes. In all I have 80 coins. How many have I of each?

4. Divide $10 between 2 men, giving to the first $1 more than twice as much as to the second.

Let x = amount given to the second. Then 2 x + 1 = amount given to the first. Usually it is most convenient to represent the smallest quantity by x.

5. Divide $8 between 2 men, giving the first $1 less than twice as much as the second.

6. Place 11 silver coins in 2 piles, putting 3 more than 3 times as many in the first as in the second.

7. Place 24 silver coins in 2 piles, putting 4 less than 3 times as many in the first pile as in the second.

8. Divide 13 apples among 3 children, giving to the second 1 apple more than to the first, and to the third twice as many as to the first.

9. My money, increased by 4 times as much and $5 more, would equal $70. How much have I?

10. In the garden there are 4 less than 3 times as many pinks as roses. In all there are 28 flowers. How many are there of each?

Problems from Astronomy

First estimate the answers.

1. Light travels at the rate of about 186,000 miles a second. If it could travel in a curved line, how many times would it go around the earth in a second?

2. The distance to the moon is 240,000 miles. How long does it take the light which is reflected from the moon to come from the moon to the earth?

3. It is about 93,000,000 miles from the earth to the sun. How long does it take light to reach us from

the sun?

sun.

4. The planet Neptune is 2,800,000,000 miles from the At a time when it is at the same distance from the earth how long does it take light to reach us from Neptune ?

5. Venus is 67,200,000 miles from the sun. When Venus is on the side of the sun toward the earth, about how far is it from the earth?

6. When at this nearest position to the earth, how long does it take light to come from Venus to the earth?

7. The distance to the nearest fixed star is about 25,000,000,000,000 miles. How long has the light which we see in the direction of the star been traveling toward us?

8. How many times as far is it from the earth to the nearest fixed star as from the earth to the sun?

9. Sound travels in the air at the rate of about 1100 feet per second. second. How How many times faster does light travel

than sound?

10. At the rate of 1100 ft. per second, how long would it take for sound to travel from the earth to the moon?

$800

Review Problems

NEW YORK, Jan. 12, 1900. Six months after date, for value received, I promise to pay to Charles H. Sawyer, or order, Eight Hundred dollars with interest at 5 per cent per annum.

HENRY P. CLARKE.

1. Find the amount due upon the above note at the time of maturity.

The amount due is $800 plus the interest for 6 months.

2. Find what would have been due, if it had not been paid until 20 days after it became due?

3. Find the interest of a note of $400, dated Nov. 10, 1898, and paid May 5, 1900, with interest at 41%.

Find the time between the dates by the second method indicated in Book II., page 84.

4. Find the amount of a note of $225, dated July 12, 1899, and paid Oct. 1, 1900, with interest at 51%.

5. Find the amount of a note of $316, dated Nov. 17, 1898, and paid May 16, 1900, with interest at 7%.

6. What is the interest upon a note of $120.50 from Sept. 5, 1899, to Jan. 1, 1901, at 5%.

7. What sum must be invested at 5% to yield an annual income of $750?

$750 is 5% of what number?

8. When the fulcrum of a lever is between the power and the weight, and the distance of the power from the fulcrum is 4 times that of the weight from the fulcrum, how much power is necessary to raise a weight of 35 lb. 12 oz.

?

9. When the power is between the weight and the fulcrum, and the ratio of the distances from the fulcrum is as 1 to 5, how heavy must the weight be to correspond to a power of 60 pounds?