...that a proper consideration of the question may suggest, will greatly facilitate the solution. 1 . What number is that whose third part exceeds its fourth part by 16 ? Let x= the number required, Then its — part will be —x, and its — part —a;. oo 44 And...

...that a proper consideration of the question may suggest, will greatly facilitate the solution. 1 . What number is that whose third part exceeds its fourth part by 16? , Let i=the number required, Then its- part will-be-x, and its -part -a;. o tis 44 And therefore...

...-j— 1 + » Changing all the signs — 192. This shows that the question should have been as follows ; What number is that, whose third part exceeds its fourth, part by 16? 7. What number is that, T7T of which exceeds ^ of it by 18? 8. What fraction is that, to the numerator...

...3^ Changing all the signs 4 3 x — 192. This shows that the question should have been as follows ; What number is that, whose third part exceeds its fourth part by 16? 7. What number is that, T7T of which exceeds 4 of it by 18 ? 8. What fraction is that, to the numerator...

...cases, other methods of proceeding may be used ; which practice and observation alone can suggest. 1. What number is that whose third part exceeds its fourth part by 16 ? Let ¿r= the number required. Then its \ part will be \x, and its J part \x. And therefore \x...

...44x transposing, 116x=696, and .-. x=6. Questions producing equations containing fractions. Ex. 1 . What number is that whose third part exceeds its fourth part by 1 6 ? Let x = the number, then — = its third part, and — = 3 4 its fourth part, and since the difference...

...x=6. VERIFICATION. f =1 of 6=3 |=i of 6=2 l =l Therefore, -+- + 1=6, which shows that 6. is •I o truly the number sought. Again, let us endeavor to...Therefore, the excess of its third part over its fourth part xx is expressed by , which, by the question, must equal 5. xx Hence, we have the following equation...

...all the signs £—£.-, 18 4 3 a; = 192. This shows that the question should have been as follows; What number is that, whose third part exceeds its fourth part by 16? 7. What number is that, £ of which exceeds ? of it by 18? 8. What fraction is that, to the numerator...

...1, this Problem reduces to Problem 18. When 6 = 0, this Problem recíuces to Problem 26. Prob. 23. What number is that whose third part exceeds its fourth part by 16 ? Let 12x = the number. Then 4x — 3x = 16 or x = 16. Therefore the number = 12 X 16 = 192. Prob....

...= 1, this Problem reduces to Problem 18. When 6 = 0, this Problem reduces to Problem 26. Prob. 23. What number is that whose third part exceeds its fourth part by 16 ? Let 12;r = the number. Then 4x — 3x = 16 or x = 16. Therefore the number = 12 X 16 = 192. Prob....