Question 1043447: If a is added to the difference of 2 quantities, the sum is b, and if the larger is divided by the smaller, the quotient is c. Determine quantities.
Let x = larger
Let y = smaller
My attempt:
x - y + a = b
x / y = c
How do I proceed ?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x=cy from the second
substitute into the first
cy-y+a=b
y(c-1)=b-a, moving the a
y=(b-a)/(c-1), dividing both sides by (c-1)
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substitute that into the first
x-(b-a)/(c-1)=b-a
add the second term to both sides
x=(b-a)/(c-1)+(b-a)
put it over a common denominator, multiplying (b-a)(c-1) to get bc-b-ac+a
x=[1/(c-1)]{b-a+bc-b-ac+a}; the a and b cancel, and x=(bc-ac)/(c-1)
x=c(b-a)/(c-1)
Notice that x is cy
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Let x=10
y=5
a=3
10-5+3=8, so b=8
10/5=2, so c=2
See if the above formulae work
For y=(b-a)/(c-1), we get (8-3)/(2-1), and that is 5.
for x=c(b-a)/(c-1), we get 2(8-3)/(2-1)=10.
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