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two number are such that their difference their sum and their product are in the ratio of 2:11:117.the bigger number is

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Click here to see ALL problems on Numbers Word ProblemsQuestion 252310: Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number? 
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Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number?
:
Two numbers a & b
Let x = the multiplier
:
a - b = 1x
a + b = 7x
a * b = 24x
:
Add the 1st two equations
a - b = x
a + b = 7x
2a = 8x
a = 4x
or
x = .25a
:
a * b = 24x
Replace 24x; a = 4x therefore: 
a * b = 6a
b = 6
;
Using the 1st equation
a - b = 1x
Replace b with 6 and x with .25a
a - 6 = .25a
a - .25a = 6
.75a = 6
a = 
a = 8
:
Find the multiplier
a - b = x
8 - 6 = 2
:
Check this
a - b = 2 (1*2)
a + b = 14; (7*2)
a * b = 48: (24*2)
:
The numbers are 8 and 6; their products = 48

Answer 2

Two number are such that their difference their sum and their product are in the ratio of 2:11:117.the bigger number is