Mona Yahuso earns three times as much as an actuary as she does asa 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 actuary?

themediamafia73

themediamafia73

Answered question

2022-09-03

Mona Yahuso earns three times as much as an actuary as she does asa 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 actuary?

Answer & Explanation

Baluttor7

Baluttor7

Beginner2022-09-04Added 17 answers

First lets try to write equations for it. let A be what she earns as an actuary and W be what she earns as awriter, also T is her total income and B is what her brother earns.
A= 3W
A+W=T
T=40000+B
B=1/2A
ok, so lets plug in the first equation into the second.
3w+w=T
4w=T
Now the first equation into the last,
B=1/2(3w)
B=3/2w
finally lets insert the two highlighted equations into equation 3.
4w=40000+3/2w
to make it easier, lets get rid of the fraction by multilying 2 on both sides.
8w=80000+3w
-3w -3w
5w=80000/5
W=16000
since we want to get what her salary is as an actuary, plug itin.
A=3(16000)
A=48,000
she makes 48,000 as anactuary.
Daniel Paul

Daniel Paul

Beginner2022-09-05Added 3 answers

3x = earnings as an actuary
x = earnings as a writer
3x+x=Mona's total income
4x-40000=brother's income
(3x/2)=brother's income
4x-40000=(3x/2)
8x-80000=3x
5x=80000
Solve for x, then plug it in to 3x for salary as an actuary.

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