can you slove this?

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 actuary?

A.
$42,000

B.
$44,000

C.
$48,000

D.
$52,000

Answer 1

Slove? Huh? OH, you mean solve! Ok

Sounds like homework. Do it yourself.

Hints:
Brother + 40,000 = Actuary + writer
Actuary = 3 x writer
1/2 actuary = brother

Answer 2

Let the amount of money earned as an actuary for Mona Yahuso be 6 units.
Hence his brother would be 3 units.
Being a writer, she would have another 2 units.
So total earned by her would be 8 units.
8 units-3 units=5units
5 units=40000
6 units=40000 X6/5
= 48000
Therefore the answer is C.

Answer 3

for these type questions, always start by assigning a variable to the unknown you are looking for, in this case, the last line clearly tells us the unknown we are looking for is mona's salary as an actuary, so

a=mona's actuary salary

the other variables are:
w=mona's writing income
b=brother's income

the first sentence tells us that her actuary salary (a) is 3 times her writing income, algabraicly that is:

a=3w

the next sentence tells us her total income is 40,000 more than her brothers (b)

her total income is a + w
since a=3w, the total income is 3w+w=4w

total income 4w is 40,000 more than brother's income (b)

4w=b+40000

and last sentence tells us brothers earnings (b) are half as much as mona's actuary salary (a)

again, we know that a=3w, so

b= 1/2 (3w)

we now have two equations in two unknowns which is what we were looking for

4w=b+40000
b= 1/2 (3w)

there are many ways to solve these, but they all amount to about the same thing, substitution is the most straightforward

that is, since b=1/2 (3w) we will substitute that in for b in the first equation leaving us an equation with only w's

4w=1/2(3w)+40000

now a little algebra (I think you should probably be able to do this part on your own so I will go quick just so you have something to check against)

2.5w=40000
w=16000

to get a we remember that a=3w

a=48000

you can get b just for fun if you want because b=1/2(3w)

good luck

Answer 4

easy

call salary as actuary, "a", and as writer, "w". And call the brother's salary, "b".

so we know that
(1) a = 3w

so Mona's total salary, which is
a + w

is also
3w + w = 4w

we're told that this, Mona's income, is 40k more than her brother's:
(2) 4w = b + 40

finally we're told that:
(3) a = 2b

Now, from (1) and (3), which both have a on one side, we deduct that:
3w = 2b

so
b = (3/2)w

now we plug this value for b in (2):
4w = (3/2)w + 40

multiply both sides by 2:
8w = 3w + 80

subtract 3w from each side:
5w = 80

so we get:
w = 16

and from (1) we know that a = 3w, so
a = 3*16 = 48

so, answer C


incidentally, we find that:
- Mona makes a total of 64'000
- her brother makes only 24'000 (which is indeed half of what Mona makes as an actuary)

as a man, I find this a very (female) chauvinistic problem, by the way ;-)

Answer 5

mona actuary, x
mona writer, y
brother, z

x = 3y
x + y = 40000 + z
z = x/2

x + x/3 = 40000 + x/2
x (1 + 1/3 - 1/2) = 40000
x (6 + 2 - 3)/6 = 40000
5 x / 6 = 40000
x = 40000 * 6 / 5

x = 48,000

Check me!!

Answer 6

3W = A; A/3 = W

W + A = 40000 + B
B = 0.5(A)

A/3 + A = 40000 + 0.5(A)

A/3 + A -0.5A = 40000

A(1/3 + 1 - 1/2) = 40000
A(2/6 + 6/6 - 3/6) = 40000
A(5/6) = 40000
A = 40000 (6/5)
A = 48000.

Answer = C

Answer 7

a=3w
a+w=40,000+b
b=.5a=1.5w
substituting 1st eqn into 2nd
3w+w=b+40,000
substituting 3rd eqn int this
4w=40,000+1.5w
2.5w=40,000
w=16000 as a writer
a=3w=3*16000=48000

checking
b=a/2=48000/2=24000
a+w=b+40,000
48000+16000=24000+40000
64000=64000

answer is C. $48,000

Answer 8

C: $ 48,000

Answer 9

D. 52,000

Answer 10

c