Please help with Algebra II Word Problem?

Question

A Boy is two-thirds as old as his sister, and two years ago he was five-eighths as old as she was then. Find the their present ages.

I keep ending up with 21s=48

what am i doing wrong?

Answer 1

Girl's age now: S
Boy's age now: (2/3)S

Two years ago:
Girl's age then: S - 2
Boy's age then: (2/3)S - 2

And you are told he was 5/8 as old.

So put it all together to get:
(2/3)S - 2 = 5/8(S - 2)

Multiply both sides by 3 to get rid of the first fraction:
2S - 6 = 15/8(S - 2)

Now multiply both sides by 8 to get rid of the second fraction:
16S - 48 = 15(S - 2)

Distribute 15 through the parentheses on the right side:
16S - 48 = 15S - 30

Now subtract 15S from both sides:
S - 48 = -30

Add 48 to both sides:
S = 18

So the sister is 18 and the boy is 12. (2/3 of her age)
Two years ago they were 16 and 10. (5/8 of her age)

Answer 2

let the sister =x
Let the boy=y
the boy is 2/3x
or 2/3x=y
simplifying it we get 2x-3y=0
two years ago
the sister=x-2
the boy y-2
so since he's 5/8 of what she was 2 years ago he is
5/8(x-2)=y-2
simplifing it we get
5/8x-5/4=y-2
5/8x=y-2+5/4
5/8x=y-3/4
then we finally get
5x-8y=-6
we now have 2 equations the 1st being 2x-3y=0 and the 2nd being 5x-8y=-6
now use the elimiation method and we get
2x-3y=0
5x-8y=-6
we make x equal by multiplying the 1st equation by 5 and the 2nd by 2 and then we subtract the results of the 2 equations
we finally get
y=12 and x =18

Answer 3

2/3(x) - 5/8(x-2) = 2
16x -15(x-2) =48
x + 30 = 48
x = 18
therefore the sis is 18 and the boy is 12.

Answer 4

12 lbs. of meat and and cheese provides as much as $sixty 4.24. 4.ninety 5 for ham 6.ninety 9 for turkey 7.ninety 9 for roast 4.36 for cheese how many pounds of each and every. upload each and every of the beef up , so 'm roughing it out out to $ 30 for cheese and $34 for the beef.

Answer 5

Screw word problems. When I was in school if I could still pass a test without doing them I would skip over them

Answer 6

x = boy's age
y = sister's age

x=2/3*y
x-2=5/8*(y-2)

2/3y-2=5/8*(y-2)
16y-48=15y-30
y=18
x=36/3=13