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c = b+120
a/b = 2/3
b/c = 3/8
solve as usual, then find a+b+c
A sum of money was to be shared among 3 persons A, B, and C in the ratios 2 : 3 : 8, If C receives $120 more than B, find the sum of money shared.
oobleck
answered3 years ago
Step-by-Step Bot
answered1 year ago
Let's assume that the common ratio for the three persons is x.
According to the given ratios, the amounts received by A, B, and C can be expressed as 2x, 3x, and 8x, respectively.
We are also given that C receives $120 more than B, so we can write the equation:
8x = 3x + $120
To solve for x, we can subtract 3x from both sides of the equation:
5x = $120
Dividing both sides by 5, we find the value of x:
x = $120 / 5 = $24
Now we can find the amounts received by A, B, and C:
A = 2x = 2 * $24 = $48
B = 3x = 3 * $24 = $72
C = 8x = 8 * $24 = $192
The sum of money shared among A, B, and C is:
$48 + $72 + $192 = $312
Therefore, the sum of money shared among A, B, and C is $312.
Explain Bot
answered11 months ago
To find the sum of money shared, let's take the value of B as x dollars.
According to the given ratios, A will receive 2x dollars and C will receive 8x dollars.
It is also given that C receives $120 more than B. So, we can write the equation:
8x = x + $120
To solve this equation, we can subtract x from both sides:
7x = $120
Now divide both sides by 7:
x = $120 / 7
x ≈ $17.14
So, B receives approximately $17.14.
To find the sum of money shared, we can add the amounts received by A, B, and C:
Sum of money shared = A + B + C = 2x + x + 8x = 11x
Substituting the value of x, we get:
Sum of money shared = 11($17.14) ≈ $188.57
Therefore, the sum of money shared among A, B, and C is approximately $188.57.