FOR QUICK PERCENTAGE RESULTS.

TALK:

The pupil may become familiar with the processes and analysis of percentage problems by the use of very small numbers. Much of the work may be oral. Let him make many problems with small numbers and give solutions to them.

Anyone who has much computation to do in percentage should make use of the rules which may be deduced from the work already done. To aid in this, there follows a summary of rules with the work on one or more problems under each.

1. To find a percentage of a number. Remember:

Multiply the number by the rate in the form of a decimal or common fraction.

PROBLEM:

Find 20% of $50.

WORK:

$ 50

.20

$10.00

PROBLEM:

I pay a man 8% to collect a debt of $400. What is his commission?

WORK:

$400

.08 $32.00

PROBLEM:

A merchant told me that 60% of a shipment of 4250 bbls. flour were spoiled. How many barrels were spoiled?

WORK:

4250 bbls.

2550.00 bbls.

2. To find a number, when the rate and a percentage of the number are known.

Remember:

Divide the percentage by the rate and multiply by 100.

PROBLEM:

7% of a number is 21. What is the number?

WORK:

7) 21

3 × 100 300.

NOTE. The pupil at once sees that the quotient is 1% of the number, and 100% will be 100 times the quotient.

PROBLEM:

I invested $200 and found it was 16% of my money. How much had I?

3. To find the rate, when the number and a percentage of it are given.

Remember:

Divide the percentage by the number and reduce to hundredths.

PROFIT AND LOSS.

This is sometimes spoken of as gain and loss. The cost is taken as the basis for reckoning gain or loss.

The profit or gain is what the selling price exceeds the buying price.

The loss is what the selling price is less than the cost.

NOTE. That which costs nothing and is sold for money cannot be classed here.

PROBLEMS.

PROBLEM:

I buy wheat at 60 and sell it for 75%. What per cent do I gain?

SOLUTION:

I gain the difference between 75% and 60%, or 15. 15 is 25% of the cost. Hence, I gain 25%.

I bought flour at $3.50 per barrel. For what must I sell it to gain 20% ?

SOLUTION:

I must sell it for 100% of the cost plus 20% of the cost, or 120% of the cost.

PROBLEM:

120% of $3.50 = $4.20.

... I must sell it at $4,20.

I bought a 54 gal. barrel of syrup at 9 a gal. 10 gal. were wasted. At what must I sell the balance to gain 30% ?

The selling price is 100% of the cost + 30% of the

Syrup on hand is 54 gal. 10 gal.

= 44 gal.

The selling price of 1 gal. = 44 of $6.32, or 14. NOTE. By selling at 14, my profit would be slightly more than 25%; but for practical purposes, 14 a gal. is correct.

PROBLEM:

A manufacturer of tables makes one kind at a cost of $2.00. He sells them at a profit of 15% to the wholesale dealer. The wholesaler sells at a profit of 20% to the retailer. The retailer sells the table to his customer at a profit of 10%. What does the table cost the customer?

SOLUTION:

The manufacturer sells it for 115% of $2.00, or $2.30.

The wholesaler sells it for 120% of $2.30, or $2.76.
The retailer sells it for 110% of $2.76, or $3.04.
.. the retailer's customer pays $3.04.

NOTE. The cost to each party is the base on which he reckons his selling price.

PROBLEM:

I sold my carriage for 80% of its cost and received $90 for it. What was the cost?

SOLUTION:

1% of the cost is of $90, or $1.125.

100% of the cost = 100 x $1.125, or $112.50.

PROBLEM:

A merchant bought 90 pieces of cloth at an average cost of $3. Damage by water compelled him to sell the whole at a loss of $27. The selling price was what per cent of the cost!

SOLUTION:

=

The cost 90 $3, or $270.

The selling price was $270 - $27, or $243.
$270 = 100% of cost.

$1 = 2 of 100% of cost, or 19% of cost.

$243 = 243 × 14% of cost, or 90% of cost.

NOTE. This may be given in the way here: "The selling price is as many per cent of the cost as $243 $270, or 90."

PROBLEM:

A jeweler sold two watches at $20 each. he lost 25% and on the other he gained 25%. did each cost?

SOLUTION:

On the first 75% of cost = $20.
The cost was of $20, or $26}.
On the second 125% of cost = $20.
The cost was of $20, or $16.

On one

What

COMMISSION.

Sometimes one man sells goods owned by another, and for his work receives a part of what the goods bring. In such cases, he is said to sell on commission.

Commission is the sum paid an agent for transacting or doing business. If goods are bought, commission is a percentage of the cost of the goods. If goods are sold, commission is a percentage of the money received for the goods. If a collection is made, commission is a percentage of the amount collected.

A commission merchant is one who sells goods for another on commission. He is sometimes called a factor. He usually has temporary possession of