KEY TO DODD'S ALGEBRA.

PROBLEMS

In Simple Equations of one Unknown Quantity.

1. What number is that to the double of which if 13 be added, the sum will be 75?

Let x represent the number; then

2x represents double the number;

and by the conditions of the problem, the Equation will be

2x+13=75.

This Equation will give x=31.

2. Find a number such that if it be multiplied by 5, and 24 be subtracted from the product, the remainder will be 36.

Let x represent the number; then

5x represents 5 times the number;

and by the conditions of the problem, the Equation will be

which will give x=12.

5–24=36;

3. What number is that to of which if 25 be added, the sum obtained will be equal to the number itself minus 39 ?

4. Find a number such that if of it be subtracted from three times the number, the remainder will be 77.

from which the value of x will be found equal to 28.

5. Find what number added to the sum of one half, one third, and one fourth of itself will be equal to 4 added to twice the number. Let x represent the number; then

X represents one half of the number;

2

and, by the conditions of the problem, the Equation will be

6. Divide the number 165 into two such parts, that the less may be equal to of the greater.

This Equation will give x= 15, the less part; hence 165-15=150 is the greater.

7. Divide the number 100 into two such parts that six times the less may be equal to twice the greater.

Let x represent the less part; then
100-x represents the greater;
6x represents 6 times the less; and
200-2x represents twice the greater.
We shall then have the Equation

6x=200-2x;

which will give r= 25, the less part; hence 100-25=75 is the greater.

8. It is required to divide 75 into two such parts that 3 times the greater may exceed 7 times the less by 15.

Let x represent the less part; then

75-x represents the greater;

225-3x represents 3 times the greater; and
7x represents 7 times the less.

The Equation will then be

225-3x=7x+15.

This Equation will give x=21, the less part; hence 75-21=54 is the greater.

9. What sum of money is that to which if $100 be added, of the amount will be $400 ?

=400;

10. A prize of $100 is to be divided between two persons-the share of the first being of that of the other. What are the shares?

Let x represent the share of the second; then

100-x represents the share of the first;

from which will be found = $561, the share of the second; hence 100—561=$432, the share of the first.

11. A post has of its length in the mud,

of it in the water, and

15 feet above the water. What is the length of the post?

12. Find a number such that if it be divided by 12, the divisor, dividend, and quotient together shall make 64.

was wine, and part minus 5 gallons was cider. What was the whole

number of gallons in the mixture?