SOLUTION: If X + 3 : 4 x + 1 is the duplicate ratio of 3 : 5 find the value of x

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Question 1086490: If X + 3 : 4 x + 1 is the duplicate ratio of 3 : 5 find the value of x
Found 2 solutions by MathLover1, Shin123:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x+%2B+3%29%3A%284+x+%2B+1%29 is the duplicate ratio of %283+%3A+5+%29, we have
%28x+%2B+3%29%3A%284+x+%2B+1%29=2%283+%3A+5+%29
%28x+%2B+3%29%2F%284+x+%2B+1%29=2%283%2F5+%29
%28x+%2B+3%29%2F%284+x+%2B+1%29=6+%2F5
5%28x+%2B+3%29=6+%284+x+%2B+1%29
5x+%2B+15+=24x+%2B+6
15-6+=24x+-5x
9+=19x
highlight%28x=9%2F19%29

check the ratio:
%289+%2F19+%2B+3%29%2F%284+%289+%2F19%29+%2B+1%29
%289+%2F19+%2B+57%2F19%29%2F%2836%2F19%2B+19%2F19%29
%2866%2F19%29%2F%2855%2F19%29
66%2F55..............66%2F55=%2866%2F11%29%2F%2855%2F11%29=6%2F5
6%2F5 which is the duplicate ratio of %283+%3A+5+%29

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%2F%284x%2B1%29=3%2F5
3%284x%2B1%29=5%28x%2B3%29
12x%2B3=5x%2B15
7x%2B3=15
7x=12
highlight%28x=12%2F7%29 Check:
%2812%2F7%2B3%29%2F4%2812%2F7%29%2B1=3%2F5
%2812%2F7%2B21%2F7%29%2F%2848%2F7%2B7%2F7%29=3%2F5 Tutor @MathHelper1 made a mistake as by writing 6/5 instead of 3/5.
%2833%2F7%29%2F%2855%2F7%29=3%2F5
33%2F55=3%2F5
highlight%283%2F5=3%2F5%29