Find two consecutive odd numbers that add to 208, when the smaller number is added to five times the larger number.
results of the three different options by showing the step by step calculations
option 1-6%compounded interest quarterly for 5 years
option 2- 8%compound interest annually for 5 years
option 3-14.5%simple interest for 10 years
n + 5(n+2) = 208
6n+10 = 208
6n = 198
n = 33
he numbers are 33 and 35
33 + 175 = 208
To find two consecutive odd numbers that satisfy the given conditions, we need to set up an equation based on the information provided.
Let's assume that the smaller odd number is represented by 'x', and the next consecutive odd number is 'x + 2'.
According to the problem, the sum of these two numbers is 208:
x + (x + 2) = 208
To simplify this equation, combine like terms:
2x + 2 = 208
Now, let's incorporate the second part of the problem, which states that the smaller number added to five times the larger number also equals 208. Mathematically, this can be represented as:
x + 5(x + 2) = 208
To solve this equation, apply the distributive property:
x + 5x + 10 = 208
Combine like terms:
6x + 10 = 208
Now, we can solve for 'x':
6x = 208 - 10
6x = 198
x = 198 / 6
x = 33
We have found that the smaller odd number is 33. To find the next consecutive odd number, substitute 'x' into the equation:
x + 2 = 33 + 2 = 35
Therefore, the two consecutive odd numbers that add up to 208 when the smaller number is added to five times the larger number are 33 and 35.