...from 10, and multiply the remainder by the number itself, the product shall be 21. Ans. 7 or 3. 11. To divide 100 into two such parts, that the sum of their square roots may be 14. Ans. 64 and 36. 12. It is required to divide the number 24 into two such parts, that their product may be equal to...

...of which the first is to the third as 5 to 9, and the sum of all three is 63. Ans. 1 <, 21, 27. 22. It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided...

...progression, of which the first is to the third as 5 to 9,and the sum of all three is 63? Ans. 15, 21,27. 22. It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided...

...lew ; v by theprob.x1 4 -- =ic,'.-i=^/ -- ,bx <2x = 12, and— =—=8. a 3 28. Divide the number 25 into two such parts, that the sum of their square roots may be 7. Let o=25, fc=7. x=one part, then a—x=the other, v by theprob. ^x+ ^/a—x=b; square both sides,...

...10, aijd then multiply the remainder by the number itself, the product shall be 21. Ans. 7 or 3. 3. It is required to divide the number 24 into two such parts, that their product shall be equal to 35 times their difference. Ans. 10 and 14 4. It is required to divide a line, of...

...18 x (x-yY = 7'2, or (xy)*=4 ; .:xy = 2. Again, x1— and 4xy =96. _12_ .. r~~ > but xy =2; Ex. 6. To divide the number 24 into two such parts, that their product shall, be to thesîora of their squares : : 3': 10. ANSWER, 18 and 6. Ex. 7. There are two numbers...

...which the first is to the third as 5 to 9, and the sum of all three is 63 ? Ans. 15, 21, 27. 22. lt is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided...

...of two numbers being given ; to find the numbers. Ans. a — V6 — a2 and 141. To divide the number 100 into two such parts, that the sum of their square roots may be 14. Jlns. 64 and 36. 142. To find three such numbers, that the sum of the first and second multiplied into...

...y== 1,and y = 4 + \/ | ; consequently o; (1+J/) =! + \/£• PROBLEM LI. To divide the number 100 (a} into two such parts, that the sum of their square roots may be 14 (bJ * Let the greater part be x, and the lesser will be a — x ; therefore, ly the problem, \/ x +...

...THEOR. 1, 18 x(x— j/)'=72, Again, x*—2xу+у'=4, and 4xy =96. or ж+^=ю,| but x— y=2 ; Ex. 6. To divide the number 24 into two such parts, that their product shall be to the sum of their squares : : 3 : 10. : ANSWER, 18 and 6. Ex. 7. There are two numbers which...