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Question 475342: sum,difference and product of two no are in the ratio 1:11:90 then what is the bigger no
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ratio is 1:11:90
let a equal the first number and let b equal the second number.
the sum is equal to a+b
the difference is equal to a-b
the product is equal to a*b
the first ratio is 1:11 which means:
(a+b)/(a-b) = 1/11
that means that the sum is to the difference as 1 is to 11.
if you cross multiply this ratio then you get:"
(a+b) * 11 = (a-b)
perform the indicated operations and you get:
11a + 11b = a - b
subtract a from both sides of the equation and subtract 11b from both sides of the equation and you get:
10a = -12b
divide both sides of the equation by 10 and you get:
a = -12b/10 which becomes:
a = -1.2b
now look at the ratio of the difference to the product.
that ratio is 11/90.
that means that:
(a-b)/(a*b) = 11/90.
we already know that a is equal to -1.2b so we can substitute in this equation to get:
(-1.2b - b) / ((-1.2b)*b) = 11/90
simplify to get:
-2.2b/-1.2b^2 = 11/90
simplify further to get:
-2.2/-1.2b = 11/90
multiply both sides of this equation by b and you get:
-2.2/-1.2 = 11/90 * b
multiply both sides of this equation by 90/11 andyou get:
90/11 * -2.2 / -1.2 = b
simplify this to get:
b = 15
since a = -1.2 * b, this makes:
a = -18
that should be your answer.
confirm this answer is correct by plugging these values into the original expressions to see if the ratios hold true.
a + b becomes -18 + 15 which equals -3.
a - b becomes -18 - 15 which equals -33.
a * b becomes -18 * 15 which equals -270
plug these numbers into your ratios and you'll see the following:
-3/-33 = 1/11 which is the ratio of the sum to the difference.
-3/-270 = 1/90 which is the ratio of the sum to the product.
-33/-270 = 11/90 which is the ratio of the difference to the product.
the ratio as shown is another way of saying:
the difference is equal to 11/1 times the sum.
the product is equal to 90/1 times the sum.
the product is equal to 90/11 times the difference.
The answer to the question would be:
a = -18
b = 15
the larger number is therefore 15 because 15 is greater than -18.
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