SOLUTION: Seventy eight is divided into two parts such that five times the first part and fourtimes the second part are in the ratio 15:14.Find the first part a)32 b)36 c)42 d)46

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Question 138303: Seventy eight is divided into two parts such that five times the first part and fourtimes the second part are in the ratio 15:14.Find the first part
a)32 b)36 c)42 d)46
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tow parts be x and y.
Given: x+%2B+y+=+78 and 5x%2F4y+=+15%2F14
5x%2F4y+=+15%2F14
5x+=+%2815%2A4y%29%2F14
x+=+%2815%2A4y%29%2F%2814%2A5%29
x+=+%283%2A2y%29%2F7
x+=+6y%2F7 --> 7x%2F6+=+y
Substitute in the first euwation:
x+%2B+y+=+78
x+%2B+7x%2F6=+78
6x+%2B+7x+=+468
13x+=+468
x+=+36
Check your answer:
x+%2B+y+=+78
36+%2B+y+=+78
y+=+42
IS the ratio of 5x/4y = 15/14?? %285%2A36%29%2F%284%2A42%29 = 180%2F168 = 15/14 Check!