Algebra (Page 12)

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Exercise 4.

Illustrative Example. The sum of two numbers is 25, and the larger is 3 less
than three times the smaller. What are the numbers?

Solution.

Let x=smaller number,
3x ¡ 3=larger number.
x + 3x ¡ 3=25
4x ¡ 3=25
4x=282
x=7
3x ¡ 3=18

The numbers are 7 and 18.

1. Charles and Henry together have 49 marbles, and Charles has twice as
many as Henry and 4 more. How many marbles has each?

2. In an orchard containing 33 trees the number of pear trees is 5 more than
three times the number of apple trees. How many are there of each kind?

3. John and Mary gathered 23 quarts of nuts. John gathered 2 quarts more
than twice as many as Mary. How many quarts did each gather?

4. To the double of a number I add 17 and obtain as a result 147. What is
the number?

5. To four times a number I add 23 and obtain 95. What is the number?

6. From three times a number I take 25 and obtain 47. What is the number?

7. Find a number which being multiplied by 5 and having 14 added to the
product will equal 69.

8. I bought some tea and co®ee for $10.39. If I paid for the tea 61 cents more
than ¯ve times as much as for the co®ee, how much did I pay for each?

9. Two houses together contain 48 rooms. If the second house has 3 more
than twice as many rooms as the ¯rst, how many rooms has each house?
Illustrative Example. Mr. Y gave $6 to his three boys. To the second he
gave 25 cents more than to the third, and to the ¯rst three times as much
as to the second. How much did each receive?

Solution.


2Is the same principle applied here that is applied on page 12?

12

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