I. A, wishing to sell a cow and a horse to B, asked 150% more for the horse than for the cow; he then reduced the price of the cow 25%, and the horse 334%, at which price B took them, paying $290; what was the price of each? (1.) (2) 100% asking price of the cow. Then 1. 100%=250%, 2. 1% 1 of 250%=2.50%, and (4.) 3. 33% 33 times 2.5%=833% reduction on the asking price of the horse. 250%-83%=1663 %=selling price of the horse. .. 241% $290, 75% 75 times$ 1.20-$90-selling price of the COW. 166% 1663 times $1.20 $200-selling price of the horse. $ 90-selling price of the cow, and (Brooks' H. A., p. 243, prob. 18.) I. A mechanic contracts to supply dressed stone for a church for $87560, if the rough stone cost him 18 cents a cubic foot; but if he can get it for 16 cents a cubic foot, he will deduct 5% from his bill; required the number of cubic feet and the charge for dressing the stone. 2. 1% of $87560-$875.60, and 3. 5%-5 times $875.60-$4378 the deduction. 4. 18-169-27=the deduction per cubic foot. II. 5. .. $4378=the deduction of 4378÷.02, or 218900 cubic feet. Then 6. $87560 cost of 218900 cubic feet. 7. $.40 $87560÷÷218900-cost of one cubic feet. 18... $.40-$.18-$.22-cost of dressing per cubic foot. III...< 218900 number of cubic feet, and 22 cents=cost of dressing per cubic foot. (Brooks' H. A., p. 241, prob. 21.) EXAMPLES. 1. A merchant, having $1728 in the Union Bank, wishes to withdraw 15%; how much will remain? Ans. $1468.80. 2. A Colonel whose regiment consisted of 900 men, lost 8% of them in battle, and 50% of the remainder by sickness; how many had he left? Ans. 414 men. 3. What % of $150 is 25% of $36? 4. What % of 1 of 4 of § is ? Ans. 6%. Ans. 314%. 5. If a man owning 45% of a mill, should sell 33% of his share for $450; what would be the value of the mill? Ans. $3000. 6. A. expends in a week $24, which exceeds by 33% his earnings in the same time. What were his earnings? Ans. $18. 7. Bought a carriage for $123.06, which was 16% less than I paid for a horse; what did I pay for the horse? Ans. $146.50. 8. Bought a horse, buggy, and harness for $500. The horse cost 37% less than the buggy, and the harness cost 70% less than the horse; what was the price of each? Ans. buggy $27525, horse $17213, and harness $5121. 9. I have 20 yards of yard-wide cloth, which will shrink on sponging 4% in length and 5% in width; how much less than 20 square yards will there be after sponging? Ans. 18 yards. Ans. ∞. 10. A. found $5; what was his gain %? 11. The population of a city whose gain of inhabitants in 5 years has been 25%, is 87500; what was it 5 years ago? Ans. 70000. 12. The square root of 2 is what % of the square root of 3? Ans. √6X331%. 13. A laborer had his wages twice reduced 10%; what did he receive before the reduction, if he now receives $2.02 per day? Ans. $2.50. 14. The cube root of 2985984 is what % of the square root of the same number? Ans. 8%. 15. A man sold two horses for the same price $210; on one he gained 25%, and on the other he lost 25%; how much did he gain, supposing the second horse cost him as much as the first? Ans. $10. 16. A merchant sold goods at 20% gain, but had it cost him $49 more he would have lost 15% by selling at the same price; what did the goods cost him? Ans. $119. 17. If an article had cost 20% more, the gain would have been 25% less; what was the gain %? Ans. 50%. II. COMMISSION. 1. Commission is the percentage paid to an agent for the transaction of business. It is computed on the actual amount of the sale. 2. An Agent, Factor, or Commission Merchant, is a person who transacts business for another. 3. The Net Proceeds is the sum left after the commission and charges have been deducted from the amount of the sales or collections. 4. The Entire Cost is the sum obtained by adding the commission and charges to the amount of a purchase. I. An agent received $210 with which to buy goods; after deducting his commission of 5%, what sum must he expend? 1. 100% what he must expend. 2. 5% his commission. 3. 100% +5%-105%-what he receives. II.4. $210=what he receives. 5... 105% $210, 6. 1% 7. 100% of $210-$2, and 100 times $2-$200=what he expends. III. .. $200=what he must expend. (R. 3d p., p. 207, prob. 4.) Note.-Since the agent's commission is in the $210, we must not take 5% of $210; for we would be computing commission on his commission. Thus, 5% of ($200+$10)=$10+$.50. This is $.50 to much I. An agent sold my corn, and after reserving his commission, invested the proceeds in corn at the same price; his commission, buying and selling was 3%, and his whole charge $12; for what was the corn first sold? (3.) II. cost of the corn. 3% the commission. 100%-3%-97%=net proceeds, which he invested 3. 100%+3%=103% entire cost of second lot of 4. corn. 97% entire cost of second lot of corn. (4.) 5... 103%=97%, 6. 1% of 97%=19%%%, and 103 = 103 7. 100% 100 times 97% 94,18%-cost of second lot of corn in terms of the first. 97 85 103 3%-3 times 195%%=215%%= commission on second lot. 3%+218%%-5%%%-whole commission. $12 whole commission. 1 of $12-$2.06, and .. 5,85%-$12, 85 103 (9.) 100% 100 times $2 06-$206=cost of first lot of corn III. ... $206=cost of first lot of corn. (R. H. A., p. 219, prob. 10.) I. Sold cotton on commission, at 5%; invested the net proceeds in sugar, commission, 2%; my whole commission was $210; what was the value of the cotton and sugar? (1.) 100% cost of cotton. (2.) (3.) 5% commission. [vested in sugar. 100%-5%-95%-net proceeds, which he in II. 100 times 5%-937% cost of sugar in terms of cotton. 2%-2 times%%% =144% commission on the sugar. 5%+144%-644%=whole commission. $210 whole commission. 100% 100 times $30.60-$3060-cost of cotton. 1%-937 times $30.60 $2850=cost of sugar. cost of cotton, and $2850 cost of sugar. (R. H. A., p. 219, prob. 6.) I. A lawyer received $11.25 for collecting a debt; his com mission being 5%; what was the amount of the debt? $11.25. of $11.25-$2.25, and 100 times $2.25 $225=amount of the debt. amount of debt. (R, 3d p., p. 207, prob. 6.) I. Charge $52.50 for collecting a debt of $525; what was the rate of commission? 1. $525=100%. II.2. $1 of 100%-21%, and. L3. $52.50 52.5 times 1%-10%=rate of commission. III... 10% rate of commission. I. My agent sold my flour at 4% commission; increasing the proceeds by $4.20, I ordered the purchase of wheat at 2% commission; after which, wheat declining 3%, my whole loss was $5; what was the flour worth? 2. 2% commission on wheat. 3. 100%+2%=102% entire cost of wheat. 4. 96%+$4.20 entire cost of wheat. 5... 102% 96% +$4.20, 6. 1% of (96%+$4.20 ) =.94%+$.04111, 8. 2%-2 times (.94%+$.04111%)=115%+$.08. 1. 100% 94,2% +$4.111%, 3. 33% 3 times (1%+$.047)=3%+$.1337= loss on wheat. 4% +115% +$.0817+351% +$.1337=95%+ $.21 whole loss. (7.) (8.) (9.) |