Ex. 5. A is twice as old as B ; ten years ago he was four times as old ; what are their present ages ?
Let x represent B's age in years, then 2 x represents A's age.
Ten years ago their ages were respectively, x — 10 and 2x — 10 years ; thus we have 2x — 10 = 4(x — 10) ; 2 x- 10 = 4 x - 40, 2x= 30 ; x = 15,
so that B is 15 years old, A 30 years.
Note. In the above examples the unknown quantity x represents a number of dollars, ducks, years, etc, ; and the student must be careful to avoid beginning a solution with a supposition of the kind, " let x = A's share," or "let x = the ducks," or any statement so vague and inexact.
EXAMPLES IX.
1. One number exceeds another by 5, and their sum is 29; find them. 2. The difference between two numbers is 8; if 2 be added to the greater the result will be three times the smaller; find the numbers, 3. Find a number such that its excess over 50 may be greater by 11 than its defect from 89. 4. What number is that which exceeds 8 by as much as its double exceeds 20? 5. Find the number which multiplied by 4 exceeds 40 as much as 40 exceeds the original number. 6. A man walks 10 miles, then travels a certain distance by train, and then twice as far by coach. If the whole journey is 70 miles, how far does he travel by train ? 7. What two numbers are those whose sum is 58, and difference 28? 8. If 288 be added to a certain number, the result will be equal to three times the excess of the number over 12; find the number, 9. Twenty-three times a certain number is as much above 14 as 16 is above seven times the number; find it. 10. Divide 105 into two parts, one of which diminished by 20 shall be equal to the other diminished by 15. 11. Divide 128 into two parts, one of which is three times as large as the other. 12. Find three consecutive numbers whose sum shall equal 84.
