Algebra Problem that I cannot solve?

Question

Mona Yahuso earns three times as much as an actuary as she does as a writer. Her total income is $40,000 more than that of her brother. He earns half as much as Mona does as an actuary. What is Mona's salary as an actaury?

USE ONLY ONE VARIABLE, and show work

Answer 1

Writer = x
Actuary = 3x
3x + x = 4x
Brother = 3x/2 = 4x - 40000
3x/2 = 4x - 40000
3x = 8x - 80000
3x - 8x = -80000
-5x = -80000
5x = 80000
x = 80000/5
x = 16000
Actuary = 3x
= 3*16000
= $48000

Answer 2

I'm guessing Mona works as both an actuary and a writer.
Her income as a writer is x, as an actuary 3x
so her total income is x + 3x = 4x
her brother earns (3x)/2 and Mona makes 40000 more than this.

so 4x = 40000 + 3x/2
x = 40000/(4-3/2) = 16,000

actuary salary = 3x = 3(16000) = 48,000

Answer 3

Let Mona's writer salary = x. This means her actuary salary is 3x, and her total salary is x + 3x, or 4x.

Her brother earns half her actuarial salary, or 1.5x, and this is $40,000 less than Mona's total salary. So we have this formula:

1.5x + 40,000 = 4x

Now you can easily solve for x, then find Mona's actuary salary (remembering that her actuary salary is 3x).

40,000 = 2.5x
x = 16,000
3x = 48,000 <<< YOUR ANSWER

Now let's check our answers to see if they make sense given the original problem:

16,000 = writer salary
48,000 = actuarial salary
64,000 = total salary

1/2 * 48,000 = 24,000 = brother's salary

64,000-24,000 = 40,000 mona's salary greater than brother's salary

So, it all checks out!

~ ♥ ~

EDITED TO ADD: Several folks are making the mistake in taking the brother's salary as 1/2 Mona's total salary, rather than 1/2 Mona's actuarial salary, so be careful when choosing which one of these answers you use! ($48,000 is the right answer!)

Answer 4

ok so the variable will be called x, and since everything is based on mona's salary as an actuary, her salary as an actuary will be x.
mona's salary as an actuary=3(mona's salary as a writer) x=3(mona's salary as a writer)
(mona's salary as a writer)=x/3
mona's total income=x+(x/3)=(4/3)x
mona's total income=mona's brother's income+40,000
(4/3)x=mona's brother's income+40,000
mona's brother's income=(4/3)x-40,000
mona's brother's income=(1/2)(mona's salary as an actuary)
mona's brother's income=(1/2)x
(1/2)x=(4/3)x-40,000
x=(8/3)x-20,000
x=x[(8/3-5/3)]---->(8/3)-(5/3)=(3/3)=1
x=(8/3)x-(5/3)x
20,000=(5/3)x
multiply both sides by 3/5 and you get
x=$12,000

Answer 5

A = her income as an actuary.
A/3 = her income as a writer
A/2 = her brother's income as an actuary

(A + 1/3 A) = (1/2)A + 40,000
(4/3)A - (1/2)A = 40,000
(8/6 - 3/6)A = 40,000
(5/6)A = 40,000
A = (6/5)40,000 = 48,000

Answer 6

Mona's total salary = m, and her actuarial salary is 3/4 m.

Mona earns 40000 more than her brother, who earn half what she does. So 40000 = 1/2 m, and m = 80000.

3/4 m = 3/4 of 80000, which is 60000, her actuarial salary. The other 20000 comes from writing.

Answer 7

3x + x = 40,000 +3/2x where "x" is how much she makes as a writer.

3/2x is the amount her brother makes. Three times the writing but half as much.

3x + x is the actuary plus the writing.

4x -3/2x = 40,000 subtracting 3/2x from both sides.
5/2x =40,000 mutliply both sides by two and divide both sides by 5....
x=16,000 where 'x' is the amount she makes from writing. Her actuary salary is three times her writing, or $48,000

She makes $48,000 from an actuary and $16,000 as a writer.

Her brother makes $24,000..

You really have to read the algerbra questions carefully.

Answer 8

put the salary of the actuary as the variable, i shall use "a"
3a = salary as a writer

so,
a + 3a = 40000 + (1/2)a
4a = 40000 + (1/2)a
3.5a = 40000
a = 11428.57 dollars

Answer 9

3w (act) + w (writ) = mona
mona = 40k + bro
bro = .5(3w) = 1.5 w

1st eq w/ substitutions
3w + w = 40k + 1.5w
4w = 40k + 1.5 w
2.5w = 40,000
w = 16000 ....... 3w = 48000 .... 1.5w = 24,000

so ...48k + 16k = 64k (40k more than bro)