Mr. Yeo saved 1/12 of his salary, spent another 1/4 of it then and divided the rest among his family. Each family member received 1/9 of his salary. Find the numbers of family members that receives 1/9 of his salary.
1/12 + 1/4 = 1/3, leaving 2/3 = 6/9
so, what do you think?
Step 1: Let's assume Mr. Yeo's salary as 'S'.
Step 2: Mr. Yeo saved 1/12 of his salary, so the amount saved is (1/12) * S.
Step 3: Mr. Yeo spent another 1/4 of his salary, so the amount spent is (1/4) * S.
Step 4: The amount left after saving and spending is S - [(1/12) * S + (1/4) * S] = S - (1/12 + 1/4) * S = S - (1/12 + 3/12) * S = S - (4/12) * S = S - (1/3) * S = (2/3) * S.
Step 5: Mr. Yeo divided the remaining amount among his family members, and each family member received 1/9 of his salary. Let's assume there are 'N' family members.
Step 6: This means each family member received (1/9) * (2/3) * S = (2/27) * S.
Step 7: To find the number of family members, we need to divide the total amount divided among the family members ((2/3) * S) by the amount received by each member ((2/27) * S).
So, N = (2/3) * S / (2/27) * S.
Simplify the above expression:
N = (2/3) * S * (27/2) * S = 27/3 = 9.
Therefore, there are 9 family members who received 1/9 of Mr. Yeo's salary.
To find the number of family members that received 1/9 of Mr. Yeo's salary, we first need to determine the portion of his salary that he had left after saving 1/12 and spending 1/4 of it.
Let's start with the given information:
- Mr. Yeo saved 1/12 of his salary
- He spent another 1/4 of it
- The rest was divided among his family members, and each received 1/9 of his salary
Let's assume Mr. Yeo's salary is represented by the variable "S."
Amount saved = 1/12 * S
Amount spent = 1/4 * S
Amount left after saving and spending = S - (1/12 * S) - (1/4 * S)
Combining like terms, we can simplify the equation:
Amount left after saving and spending = S - (1/12 + 1/4) * S
Amount left after saving and spending = S - (1/12 + 3/12) * S
Amount left after saving and spending = S - (4/12) * S
Amount left after saving and spending = S - (1/3) * S
Amount left after saving and spending = S - S/3
Amount left after saving and spending = (3S - S)/3
Amount left after saving and spending = 2S/3
Since the remaining amount is divided equally among the family members who each receive 1/9 of his salary, we can set up the following equation:
(2S/3) / N = 1/9
Here, N represents the number of family members.
To solve for N, we can multiply both sides of the equation by 9, then divide both sides by 1/9 (or multiply by its reciprocal).
(2S/3) / N = 1/9
9 * [(2S/3) / N] = 9 * (1/9)
(18S/3) / N = 1
(6S/3) / N = 1
(2S/3) / N = 1
We can see that (2S/3) divided by N must be equal to 1.
Therefore, the number of family members that received 1/9 of Mr. Yeo's salary is N = 3.
Hence, there are 3 family members.