Mona earns 3 times as much as an actuary as she does as a writer. Her total income is $40,000 more than her brother. He earns half as much as Mona does as an actuary. What is Mona's salary as an actuary?
Mona's salary as writer --- x
salary as actuary -- 3x
brother's salary = 3x/2
"Her total income is $40,000 more than her brother."
---> x + 3x = 3x/2 + 40000
4x - 1.5x = 40000
2.5x = 40000
x = 16000
Mona as writer --- 16000
Mona as actuary --- 48000
brother -----24000
All information checks
Well, it sounds like Mona has quite the interesting career(s) going on! Let's see if we can unravel this salary mystery, shall we?
Let's call Mona's salary as a writer "W" and her salary as an actuary "A".
According to the information given, Mona earns 3 times as much as an actuary as she does as a writer. So we can express Mona's actuarial salary as 3W, and since she earns 40,000 more than her brother, we can say that Mona's total income is A + 40,000.
Now, we know that Mona's brother earns half as much as Mona does as an actuary. Therefore, we can say Mona's brother's income is (1/2)A.
Putting it all together, we have the equation:
A + 40,000 = 3W + (1/2)A
Now, let's harness the power of mathematics to solve this equation and find Mona's salary as an actuary:
A - (1/2)A = 3W - 40,000
Simplifying, we get:
(1/2)A = 3W - 40,000
Now, multiplying both sides of the equation by 2 to get rid of that pesky fraction:
A = 6W - 80,000
And voila! We have the equation that represents Mona's salary as an actuary. Unfortunately, without additional information regarding Mona's total income, we won't be able to determine Mona's exact salary as an actuary. But hey, at least we had some mathematical fun along the way, right?
Let's assume Mona's salary as a writer is x dollars.
According to the given information, Mona earns 3 times as much as an actuary as she does as a writer. Therefore, her salary as an actuary would be 3x dollars.
Her brother earns half as much as Mona does as an actuary. Therefore, her brother's salary would be (1/2) * 3x = (3/2)x dollars.
Her total income is $40,000 more than her brother's income. Therefore, we can write the equation:
3x + 40,000 = (3/2)x
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
6x + 80,000 = 3x
Subtracting 3x from both sides of the equation, we get:
3x + 80,000 = 0
Subtracting 80,000 from both sides of the equation, we get:
3x = -80,000
Dividing both sides of the equation by 3, we get:
x = -80,000 / 3
x = -26,666.67
Since salary cannot be negative, we'll consider the positive value of x. Therefore, Mona's salary as an actuary is:
3x = 3 * (-26,666.67) = -$80,000
However, it seems like there might be an error in the given information or calculation. Please double-check the information provided to solve the question accurately.
To find Mona's salary as an actuary, let's break down the information given step by step:
Let's assume Mona's salary as a writer is represented by x.
According to the question, Mona earns 3 times as much as an actuary as she does as a writer. So, her salary as an actuary will be 3x.
Her brother's salary is $40,000 less than her total income. Therefore, her brother's salary can be represented as (3x + x) - $40,000.
Additionally, the question states that her brother earns half as much as Mona does as an actuary. So, her brother's salary can also be represented as (1/2) * (3x) = (3x/2).
Equating the two representations of her brother's salary, we have:
(3x + x) - $40,000 = (3x/2)
Simplifying the equation:
4x - $40,000 = (3x/2)
To continue solving this equation, we can multiply both sides of the equation by 2 to eliminate the fraction:
2 * (4x - $40,000) = 3x
Now distribute 2 across the brackets:
8x - $80,000 = 3x
Next, subtract 3x from both sides:
8x - 3x - $80,000 = 3x - 3x
5x - $80,000 = 0
Now, add $80,000 to both sides of the equation:
5x - $80,000 + $80,000 = $0 + $80,000
5x = $80,000
Finally, divide both sides of the equation by 5 to solve for x, which represents Mona's salary as an actuary:
5x/5 = $80,000/5
x = $16,000
Therefore, Mona's salary as an actuary is:
3x = 3 * $16,000 = $48,000