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.
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"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
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