234. Finding the Marked Price.-Merchants sometimes desire to mark articles at a price so that they may offer a given discount and sell them at some assigned net price. Solving equation (4), page 195, gives

235. Finding the Rate of Discount.-The wholesale merchant has a marked price in his catalogue on goods which he must sell at a given net price. He must then compute from the marked and selling price the discount rate to send to his customers. Solving equation (3), page 195, for R % gives

1. For what must an article be marked so as to permit

a discount of 20 % and still sell for $ 12?

2. What must a suit of clothes be marked so as to permit a discount of 333 % and sell for $16?

3. What must overcoats be marked to sell for $25 and still give a discount of 163 %?

4. Suits selling for $ 12 must be marked what to give a discount of 20%? of 25%? of 40 %? of 33%?

5. Canned corn sells at 24 ¢ per can or at 21 ¢ per can if bought by the dozen. What is the rate of discount when bought by the dozen? What is saved per dozen?

6. What is the rate of discount in buying canned goods at $2.25 per dozen that cost 21 ¢ per can?

7. When pencils sell at 10 ¢ each or 3 for 25 ¢, what is the rate of discount?

8. If possible, bring in data on some "special sale" that has been held in your city. Compute some rates of discount.

9. A wholesale firm finds that it must change its prices due to an advance in cost of production. How can they acquaint their customers of the changes most cheaply?

10. Tables marked $ 36 in a catalogue must be sold for $27. What will be the rate of discount?

A wholesale firm gives its customers a discount of 20% on all goods. What must be the catalogue prices of goods to sell at the following wholesale prices:

19.

Find the retailers' profit on the goods listed in Exs. 11-18 if sold at catalogue price.

20. Dining-chairs listed at $7.50 in the catalogue must be sold at $ 5.25. Find the discount rate.

21. If the chairs in Ex. 20 have advanced $1.25 each, what will be the discount rate?

22. In Ex. 20 the $1.25 is what per cent of the catalogue price of the chairs? The per cent advance of the list price plus the new discount rate equals what?

23.

Desks listed in the catalogue at $32 have increased $4 in price. What is the decrease in discount rate?

24. For what must a retail dealer sell the chairs in Ex. 20 to make a profit of 25 % on the cost?

25. For what must a dealer sell the chairs in Ex. 20 to make a profit of 25 % on the selling price?

26. Mr. Kohler's bills are due in 60 da., but he receives 4% discount by paying cash. If he pays cash for his bills, he is receiving what rate of interest on the money thus invested?

236. Discount Series. It often happens that two or more discounts are given on a bill. For instance, a bill may give a discount of 25% from the catalogue price and then 5% discount from this price if paid cash. Payment within 10 da. is reckoned as cash. It is customary to say that the discount would be 25% and 5%. Several years ago a certain firm gave three discounts on all of its catalogue goods: 70 %, 10%, and 5%.

EXERCISES

1. The catalogue price of an article is $ 12. What is the net price if the discount is 25%? Suppose that a further discount of 5% is given for cash payment, what will be the net price?

2. An article listed at $ 15 in a catalogue is subject to three discounts of 30 %, 20 %, and 10%. What will be the net price?

3.

Rewrite the bill at the top of page terms 5% cash; 2%, 30 da.; net, 60 da.

196 making the How much will it take to pay the bill within 10 da. ? 30 da.? 60 da. after purchase?

4.

Discounts of 40 %, 30 %, and 10 % are given on certain goods in a catalogue. What will be the net price of goods listed at $8? at $ 12? at $ 15? at $7?

237. One Discount Equivalent to a Series. It is often convenient to have one single discount in the place of several. The net price may be desired of each article in the bill for Ex. 3, or for each article in Ex. 4 above. It is much simpler to find the single rate of discount that is equivalent to the two or three given rates of discounts.

Let the discount series be R1, R2, and R3. Suppose that the net price after the first discount has been deducted is

N1, after the second discount has been deducted N2, and after the final discount has been deducted the net price is Nf. Equation (4) on page 195 is

The multiplier of Mp is 1, less the discount. See equation (4), page 195. Hence, (1 - R1)(1 − R2)(1 − R3) taken from 1 gives the single discount. Or,

Thus, if the discount rates are 10 %, 20 %, and 30%, the single discount rate is

1. Find the single discount equivalent to 25 % and 5% for Ex. 1 on the opposite page. Use this to find the net Is this the same as found before?

price.

2. Find the single discount equivalent to the three discounts in Ex. 2 on the opposite page.

3. Find the single discount equivalent to the three in Ex. 4 on the opposite page.

4. Show that the order of the discounts in a series is immaterial. Apply to Exs. 1 and 2 above.

5. Carry out the multiplications in equation (4) above. Verify by substituting .10, .20, and .30 for the R's.

XVIII

ACCOUNTS

238. Personal Accounts.-Merchants keep accounts with their customers who do not make all purchases for cash. The book for such accounts is called a ledger. On the left side of the page are entered goods, money, or other valuables received by the one with whom the account is kept. This is called the debit-Dr.-side. On the right side are placed payments. This is called the credit-Cr.-side.

239. Balancing Accounts. To balance an account find the difference between the debit and the credit sides and enter this in red ink on the smaller side. The sum of both sides the same-is placed below each and two lines drawn beneath this. The balance is then entered in black on the side opposite to the red entry. Balances are made monthly or when needed.