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19. A city increased 14% in population in ten years. The increase was 3332. What was the population before this increase ?

20. A city increased 16% in population in ten years. The increase was 5200. What was the population both before and after this increase ?

21. The weekly pay roll in a certain shop was increased 8%. The increase amounted to $192. What was the pay roll before the increase ?

22. The attendance at a certain school has increased 14, which is 5% of the attendance last year. What was the attendance last year?

23. A lady paid 95¢ less for groceries this week than last week. This was a decrease of 10%. How much did she pay last week ? this week ?

24. A man purchased this year 24 tons of coal less than he did last year, a reduction of 12%. How many tons did he purchase last year ? this year ?

25. In a certain month there were seven stormy days, or 25% of the total number of days. What month was it ?

26. A man sold a farm at a profit of 163% on the cost, thereby making $540. What did the farm cost him ?

27. A man has a meadow to mow. After he has mowed 24 acres, 371% of the work is done. How many acres has he then to mow ? 28. A man buying a farm is told that if he will

pay

cash he can get it for 64% less, and can thereby save $500. What would the farm then cost him ?

29. A state is building a certain number of miles of road this year. It has already finished 33% of it, or 280 miles. How many miles is it to build this year?

228. One Number is a Given Per Cent of what Number ? Because the percentage is the product of the base and the rate (5 225), therefore

The base equals the percentage divided by the rate.

For example, if 15% of a number is 390, what is th number?

390 = 15% = 39,000 + 15 = 2600. Ans. The simple equation may be used in cases of this kind, it bein explained that 2 x means 2 times some number that is to be found. For example,

0.15x = 390. Therefore

I = 2600, by dividing these equals by 0.15

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uctions profit and its of the cost of i as typical probking of goods : k goods that cost

$55. Therefore he

bargain sale for

they sold ? 1', they are sold for

hey are marked 1 did they cost ?

-120.

$160.

to mark

'le selli

EXERCISE 133

PROBLEMS WITHOUT NUMBERS

1. How do you find some required per cent of a number?
2. How do you express per cent as a decimal fraction ?
3. How do you express a decimal fraction as per cent ?
4. How do you express per cent as a common fraction ?
5. How do you express a common fraction as per cent ?

6. Name eight of the most important per cents, and the corresponding common fractions.

7. If you know the base and rate, how do you find the percentage ?

8. How do you find what per cent one number is of another?

9. How do you find the number of which a given number is a certain per cent ?

10. If you know your weight a year ago and also to-day, how do you find the gain? the per cent of gain ?

11. If you know how many pounds you have gained, and the per cent, how do you find your weight a year ago ?

12. Knowing how much a man paid for his farm, and the amount for which he is selling it, how can you find the per cent of gain or loss ?

13. Knowing that a farmer paid a certain amount for a team of horses, and sold them at a certain per cent of profit, how do you find the selling price ?

14. If a boy had a kite string of a certain length, and lost a certain

per cent of it, how do you find the amount left ? 15. If a boy had a fishing line of a certain length, and you know how many feet of it he lost, how do you find the per cent of loss ?

CHAPTER XII

PROFIT AND LOSS

229. Profit and Loss. In business transactions profit and loss are often computed as certain per cents of the cost of the property. The following may be taken as typical problems in profit and loss, including the marking of goods :

(1) At what price must a merchant mark goods that cost $275, so as to gain 20%?

If he gains 20% of $275 he gains } of $275, or $55. Therefore he must mark the goods $275 + $55, or $330.

(2) If goods marked $75 are sold at a bargain sale for 15% off the marked price, at what price are they sold ?

If the goods are sold at 15% off the marked price, they are sold for $75 less 15% of $75, or $75 - $11.25, or $63.75.

(3) If some goods are damaged so that they are marked down to $120, or 25% below cost, how much did they cost ?

100% of the cost = the cost.
25% of the cost = the loss.
75% of the cost = the selling price = $120.

1% of the cost 15 of $120.

100% of the cost 1705 (or ) of $120, or $160. (4) A dealer sold a hat that cost $2.40 so as to gain 25%. The selling price was 20% less than the marked price. What was the marked price ?

He gained 25% (or 1) of $2.40, or $0.60. Therefore the selling price was $2.40 + $0.60, or $3. Now show that

80% of the marked price the selling price $3.

1% of the marked price = go of $3.
100% of the marked price 1860 (or ) of $3, or $3.75.

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