Word problem help please?

Question

Nine pounds of sweet potatoes cost the same as 6 pounds of apples. One pound of sweet potatoes costs twice as much as a pound of onions, while a pound of apples costs 24 cents more than a pound of onions. Find the cost of each.

Answer 1

9p = 6a
1p = 2o
a = o + .24

where p = cost of sweet potatoes in $, a = cost of apples in $, and o = cost of onions in $

you have to do this by successive elimination of variables. Let's get rid of a first, in the first equation, using the last equation... so we'll substiture o + .24 for a:

9p = 6(0.24 + o)
9p = 1.44 + 6o

so now we have 2 equations with o and p, so we can solve:

since 1p = 2o, we can substitute 2o for p in our equation to get:

9(2o) = 1.44 + 6o
18o = 1.44 + 6o
12o = 1.44
o = 0.12

so a pound of onions is 12 cents

since sweet potatoes are twice that,

p = 0.24

and since apples are 24 cents more than onions,

a = 0.36


Hope this helps!

Answer 2

Let the cost of each poun of onion be x cents,Therefore the cost of 1 lb of apple is x+24 cents and that of 1 lb of sweet potato is 2x cents.According to the problem,9*2x=6(x+24) =>18x=6x+144 =>18x-6x=144 =>12x=144 =>x=144/12=12 .Therefore,cost of a pound of onion is 12 cents,that of apple is 36 cents and that of sweet potato is 24 cents.

Answer 3

let the cost of a pound of sweet potatoes be x
let the cost of a pound of apples be y and
let the cost of a pound of onions be z

We have 9x = 6y
x = 2z
and y = z+24

substituting x=2z in 9x = 6y
we have 9(2z) = 6y
18z = 6y
substitute y = z+24 in the above equation
we have 18z = 6(z+24)
= 6z + 144
bringing all terms with z to the left side, we have
18z - 6z = 144
12z = 144
z = 144/12
z= 12

the cost of a pound of onions is 12 cents
To find the cost of sweet potatoes substitute z= 12 in x= 2z
x = 2 * 12
x = 24 cents
To find the cost of apples substitute x=24 in 9x=6y or substitute z=12 in y = z+24
Either way we have, y=36 cents

Answer 4

9S=6A. S=2O. A=O+24. substituting: 9(2O)=6A, or 18O=6A. then 18O=6(O+24), so 18O=6O+144, therefore, 12O=144 so O=12. then just substitute to fine A ans S.