SOLUTION: sum,difference and product of two no are in the ratio 1:11:90 then what is the bigger no

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.

RELATED QUESTIONS
in two digits no the sum & difference of digit is 6 then the no... (answered by KMST)

two numbers are in the ratio of 3:5. if their difference is 38 what is the bigger number? (answered by ewatrrr)

The sum of two numbers is 50. The bigger number is 5 more than twice as the smaller... (answered by ikleyn)

two numbers are in the ratio 2:5. if their difference is 48,what is the bigger... (answered by htmentor,Theo,MathTherapy)

If the sum of two no. is 57 and difference is 20. What are the possible pairs. Plez help (answered by ikleyn)

difference of two natural no. are 4 and the sum of their square is 58 what the... (answered by stanbon,MathLover1)

Two numbers are in the ratio 3:5 and their sum is 112. Find the bigger number (answered by ikleyn)

the ratio of two no is 3:5, and their difference is 46. find the larger... (answered by lwsshak3)

two number has a sum of 125 and a difference of 25. What is the value of the bigger... (answered by tutoringisfun)