Given:
The sum of three numbers is 212 .
The ratio of the first to the second is 13:16 and that of the second to the third is 2:3.
To find:
The unknown numbers.
Solution:
We have,
First : Second = 13:16
Second: Third = 2:3
We need to combine these ratios, to get a single ratio for all three numbers.
Second: Third = 2×8:3×8 = 16:24
Now,
First: Second: Third = 13:16:24
Let the first, second and third numbers are 13x, 16x and 24x respectively.
So, the numbers are,
Similarly,
And,
Therefore, the three unknown numbers are 52, 64, 96.
Answer:
a. 84 < n + (n + 2) + (n + 4) < 96
b. 26 < n < 30
Step-by-step explanation:
Using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. So, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).
Since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:
84 < n + (n + 2) + (n + 4) < 96
In order to solve for 'n', we must first combine like terms:
84 < 3n + 6 < 96
Subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90
Divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.
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