A sum of money is divided between three people in the ratio 1:2:1/2. If the smallest share amounts to $48, what is the total Sum of money?
1:2:1/2
= 2:4:1 -----> ratios usually are not expressed in fraction form
let their shares be 2x, 4x, and x
but x = 48
so 2x = 96
and 4x = 192
add them up
swryhr
To find the total sum of money, we need to determine the value of the largest share.
Let's assume the smallest share is $48.
Since the ratio is given as 1:2:1/2, we can represent the shares as x, 2x, and (1/2)x.
Given that the smallest share (x) is $48, we can write the equation:
x = 48
To determine the value of the largest share, we need to find the value of 2x:
2x = 2 * 48
2x = 96
Now, let's find the value of the third share, which is (1/2)x:
(1/2)x = (1/2) * 48
(1/2)x = 24
The total sum of money is the sum of all three shares:
Total = x + 2x + (1/2)x
Total = 48 + 96 + 24
Total = 168
Therefore, the total sum of money is $168.
To determine the total sum of money, we need to determine the value of the other two shares.
Let's assume the smallest share is x dollars.
According to the given ratio, the second share is twice the smallest share, so it would be 2x dollars.
The third share is half the smallest share, so it would be (1/2)x dollars.
We know that the smallest share is $48, so we can set up an equation based on the sum of all three shares:
x + 2x + (1/2)x = Total sum of money
Combining like terms, we have:
(2 + 2 + 1/2)x = Total sum of money
(5/2)x = Total sum of money
To isolate x, we can multiply both sides by (2/5):
x = (2/5) * Total sum of money
Now, we can substitute the value of x into the equation to find the total sum of money:
48 = (2/5) * Total sum of money
To solve for Total sum of money, we can multiply both sides by (5/2):
Total sum of money = 48 * (5/2)
Total sum of money = $<<48*(5/2)=120>>120