Question 34443
Find two numbers, given that the second is 3 times the first. If you multiply the first number by the second number and the second number by 4, the sum of the products is 420.
LET FIRST NUMBER =X
SEOND NUMBER =3 TIMES FIRST =3*X
MULTIPLY THE FIRST NUMBER BY SECOND WE GET =X*3X=3X^2
MULTIPLY SECOND NUMBER BY 4 WE GET =4*3*X=12X
SUM OF 2 PRODUCTS =3X^2+12X=420...DIVIDING WITH 3 WE GET
X^2+4X=140
X^2+4X-140=0
X^2+14X-10X-140=0
X(X+14)-10(X+14)=0
(X-10)(X+14)=0
X-10=0 ....OR....X=10
SO THE 2 NUMBER ARE 10 AND 30....

OTHER POSSIBILITY IS X+14=0...OR X=-14...THE SECOND NUMBER IS -42