1. Algebra is so much like arithmetic that all that you know about addition,
subtraction, multiplication, and division, the signs that you have been using
and the ways of working out problems, will be very useful to you in this study.
There are two things the introduction of which really makes all the difference
between arithmetic and algebra. One of these is the use of letters to represent
numbers, and you will see in the following exercises that this change makes the
solution of problems much easier.
Illustrative Example. The sum of two numbers is 60, and the greater is four
times the less. What are the numbers?
Let x= the less number;
then 4x= the greater number,
and 4x + x=60,
and 4x=48. The numbers are 12 and 48.
1. The greater of two numbers is twice the less, and the sum of the numbers
is 129. What are the numbers?
2. A man bought a horse and carriage for $500, paying three times as much
for the carriage as for the horse. How much did each cost?
3. Two brothers, counting their money, found that together they had $186,
and that John had ¯ve times as much as Charles. How much had each?
4. Divide the number 64 into two parts so that one part shall be seven times
5. A man walked 24 miles in a day. If he walked twice as far in the forenoon
as in the afternoon, how far did he walk in the afternoon?