SOLUTION: two number are in the ratio of 1:11 and the their sum is 15.find the numbers.

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Question 1150838: two number are in the ratio of 1:11 and the their sum is 15.find the numbers.

Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

1.   The short solution 

The numbers are x and  11x,

where x is unknown to be found from this equation


    x + 11x = 15,

    12x     = 15

      x     =  =  = 1.25.


So, the numbers are  1.25  and  11*1.25 = 13.75.    ANSWER


2.   More detailed solution 

Let x be the smaller number.

Then the other number is 15-x,

and you have this proportion


     = .


From the proportion


    11x = 15 - x

    11x + x = 15

    12x     = 15

      x     =  =  = 1.25

and you have, finally, the same answer.


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

"two numbers are in the ratio of 1:11" which means that the second number is 11 times that of the first number.

If x is the first number, then 11*x = 11x is the second number.

"Their sum is 15", so the two numbers add to 15.
A = first number = x
B = second number = 11x
A+B = 15
x+11x = 15
12x = 15
x = 15/12 ... divide both sides by 12
x = (5*3)/(4*3)
x = 5/4
x = 1.25
A = x
A = 1.25 is the first number

Use this x value to find the value of 11x
B = 11x
B = 11*1.25
B = 13.75 is the second number

In decimal form, the two numbers are 1.25 and 13.75
In terms of fractions, the two numbers are 5/4 and 55/4

note:
13.75 = 13 + 0.75 = 13 + 3/4 = 52/4 + 3/4 = (52+3)/4 = 55/4
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