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Percentage.

222. PERCENTAGE PROBLEMS UNDER CASE I, IN WHICH

THE PER CENT IS MORE THAN 100.

Find 175% (176 or 1.75) of $632.60.

Operation No. 1.

Explanation. $6'32.60

One % of $632.60 is $6.326. 1.75

175% of $632.60 is 175 times $6.326 or

$1107.05. $31:6300

Observe that 5% of $632.60 is $31.63; $442.820

that 70% of $632.60 is $442.82; that 100% $632.60

of $632.60 is $632.60.
$1107.0500

Operation No. 2.
175% = 176 = 1 . 1 of $632.60 = $158.15.

1 of $632.60 = 7 times $158.15 or $1107.05.

PROBLEMS.

1. Find 175% of 356 ; of 276 ; of 540.20
2. Find 155% of 356 ; of 276 ; of 540.20
3. Find 145% of 356 ; of 276 ; of 540.20
4. Find 125% of 356; of 276 ; of 540.20
5. Find 200% of 356 ; of 276 ; of 540.20
6. Find 150% of 356 ; of 276 ; of 540.20
7. Find 250% of 356; of 276 ; of 540.20

(a) Find the sum of the twenty-one results.

8. David's money is equal to 150% of Henry's money. Henry has $240. How much has David ?

9. If goods cost $260, and the profit on them is 125%, what is the selling price?

10. If a Chicago lot at the beginning of a certain year was worth $8000 and during the year increased in value 50%, what was it worth at the end of the year? What would it have been worth at the end of the year had it increased 250% ? Percentage.

223. PERCENTAGE PROBLEMS UNDER CASE II, IN WHICH

THE PER CENT IS MORE THAN 100.

$1107.05 is 175% of how much money ?

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Percentage.

224. PERCENTAGE PROBLEMS UNDER CASE III, IN

WHICH THE PER CENT IS MORE THAN 100.

$1107.05 is what per cent of $632.60 ? *

Explanation.

Operation. $6.326) $1107.050 (175

6326

47445
44282

One per cent of $632.60 is $6.326 ; then $1107.05 is as many per cent of $632.60 as $6.326 is contained times in $1107.05. It is contained 175 times, so $1107.05 is 175% of $632.60.

31630
31630

NOTE.—The above problem may be solved as a similar problem is solved on page 125, Operation No. 1. $1107.05 is 1497:85 of $632.60. Perform the division indicated carrying out to hundredths only. The quotient will be 1.75 or 138 = 175%.

PROBLEMS.

1. What per cent of 845 is 2112.5 ?
2. What per cent of 845 is 1056.25 ?
3. What per cent of 845 is 1352 ?
4. What per cent of 845 is 1183 ?
5. What per cent of 845 is 2746.25,?
(a) Find the sum of the 5 answers.

6. Reuben has $2420 ; Bernie has $4961. Bernie's money equals how many per cent (hundredths) of Reuben's money?

7. A certain house cost $6425. The lot upon which it stands cost $2325. (a) The cost of the house equals how many per cent (hundredths) of the cost of the lot? (b) The cost of the lot equals how many per cent (hundredths) of the cost of the house ?

+ See "Operation and Explanation, No. 4,” page 125.

Percentage.

225. MISCELLANEOUS PROBLEMS.

1. Find 1 %* of 632; of 356 ; of 272.
2. Find 1% of 632 ; of 356 ; of 272.
3. Find .25 %t of 632; of 356 ; of 272.

(a) Find the sum of the nine results.

4. Find 34% of 496; of 532 ; of 720.
5. Find 41 % of 496 ; of 532; of 720.
6. Find 1.75% of 496 ; of 532; of 720.

(b) Find the sum of the nine results.

7. What part of 94 is 11 ? | What per cent? 8. What part of 94 is 36 ? What per cent? 9. What part of 94 is 47? What per cent? (c) Find the sum of the three “per cents.”

10. 15 is 3 % of what number? 4%? 5%? 11. 24 is 3% of what number? 4 %? 5%? 12. 42 is 3 % of what number? 4 %? 5%?

(d) Find the sum of the nine answers.

13. 375 is 125 % (136) of what number? 14. 436 is 109 % (18%) of what number? 15. 598 is 115 % (116) of what number?

(e) Find the sum of the three answers.

16. 544 is 15 % less than what number ? § 17. 545 is 25 % more than what number? 18. 510 is 170 % of what number?

(f) Find the sum of the three answers.

* This means of 1 per cent. + This means find 25 hundredths of 1 per cent. $ Answer with a common fraction in its lowest terms. $ If it is 15 per cent less than the number it is 85 per cent of the number.

Algebra.

226. TO FIND Two NUMBERS WHEN THEIR SUM AND

DIFFERENCE ARE GIVEN.

1. The difference of two numbers is 4 and their sum is 20. What are the numbers ?

Let

the smaller number, then x + 4 = the larger number,

and x + x + 4 20. Transposing x + x = 20 - 4. Uniting

2 x = Dividing

x = 8, the smaller number x + 4 = 12, the larger number.

16.

2. The difference of two numbers is 9 and their sum is 119. What are the numbers ? 3. The difference of two fractions is 20 and their sum is

What are the fractions ? 4. The difference of two numbers is d and their sum is s. What are the numbers ?

= S

Let

X = the smaller number then x + d = the larger number,

and x + x + d Transposing x + x = s-d Uniting

2 x = s

d

d Dividing

2

S
X =

Observe that any number you please may be put in the place of s; and any number less than s, in the place of d: so when the sum and the difference of two numbers are given the smaller number may be found by subtracting the difference from the sum and dividing the remainder by 2.

5. The difference of two numbers is 327, and their sum is 1159. What are the numbers ?

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