Daniel is in a choir where all of the members have a different height. When the members are numbered from 1 to n in order of increasing height, he is number n/3. When numbered in reverse order, he is member number n − 9. How many members are in the choir?
n/3 = n-10
why not n-9?
n/3 = n - (n-9)
n/3 = 9
n = 27
remember the n/3 is from the left
but (n-9) is from the right and to compare it to n/3 we have to subtract
To solve this problem, we need to set up two equations based on the information given.
Let's say there are "n" members in the choir.
According to the first piece of information, when the members are numbered from 1 to n in order of increasing height, Daniel is number n/3. This can be represented as:
n/3 = Daniel's position
According to the second piece of information, when numbered in reverse order, Daniel is member number n − 9. This can be represented as:
n - 9 = Daniel's position in reverse order
Now, we can set up an equation by equating the two expressions for Daniel's position:
n/3 = n - 9
To solve this equation, we can multiply both sides by 3 to eliminate the fraction:
3 * (n/3) = 3 * (n - 9)
n = 3n - 27
Next, we can simplify the equation:
n - 3n = -27
-2n = -27
n = (-27)/(-2)
n = 27/2
n = 13.5
However, since we are dealing with a choir, the number of members cannot be a decimal value. It must be a whole number.
Therefore, we conclude that there cannot be 13.5 members in the choir. We need to round up to the nearest whole number.
Thus, there are 𝑛 = 14 members in the choir.