Question 1177050: Hi
Rings and watches cost $10,275.00. The ratio of the number of watches to rings bought is 5:8. Each ring cost $137 more than a watch. The ratio of the total cost of the rings to watches bought was 7;8. Find the cost of a ring.
Thanks
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Rings and watches cost $10,275.00.
The ratio of the number of watches to rings bought is 5:8.
Each ring cost $137 more than a watch.
The ratio of the total cost of the rings to watches bought was 7;8
. Find the cost of a ring.
:
This problem is inconsistent.
the first ratio indicates there are more rings than watches
Then it says rings cost more than watches
the last ratio states that total cost for rings is less than total cost for watches
Can't happen!
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! this problem doesn't work out as given.
i keep getting a negative value for one of the variables.
i took a guess and figured that the ratio of watches to rings might actually be the ratio of rings to watches.
this allowed me to get a solution that made more sense because it was positive and the numbers worked out.
here's how it went after making that assumption.
let x = the number of rings.
let y = the number of watches.
let r = cost of a ring.
let w = cost of a watch.
the ratio of the number of rings to watches is 5/8.
the equation for that is x/y = 5/8.
the total cost of rings is equal to x * r.
the total cost of watches is equal to y * w.
the cost of a ring is equal to the cost of a watch plus 137 dollars.
the formula for this is r = w + 137.
you are also given that the ratio of the total cost of rings to the total cost of watches is 7/8.
the equation for this is x * r / y * w = 7/8
you have the following ratios:
x / y = 5/8
x * r / y * w = 7/8
from these ratios, you can derive the following:
x = 5/8 * y
x * r = 7/8 * y * w
you are also given that the total cost of the rings plus the total cost of the watches is 10275.
the equation for this is x * r + y * w = 10275.
since x * r = 7/8 * y * w, the equation of x * r + y * w = 10275 becomes:
7/8 * y * w + y * w = 10275.
factor out the y * w to get:
y * w * (7/8 + 1) = 10275.
since 1 = 8/8, this becomes:
y * w * (7/8 + 8/8) = 10275.
combine like terms to get:
y * w * 15/8 = 10275.
solve for y * w to get y * w = 8/15 * 10275 = 5480.
this means that x * r must be equal to 10275 - 5480 = 4795.
you now have:
x * r = 4795
y * w = 5480
since x = 5/8 * y, these equations become:
5/8 * y * r = 4795
y * w = 5480
since r = w + 137, these equations becomes:
5/8 * y * (w + 137) = 4795
y * w = 5480.
simplify these equations to get:
5/8 * y * w + 5/8 * y * 137 = 4795
y * w = 5480.
in the first of these 2 equations, replace y * w with 5480 from the second of these two equations to get:
5/8 * 5480 + 5/8 * y * 137 = 4795.
simplify to get:
3425 + 85.625 * y = 4795
subtract 3425 from both sides of this equation to get:
85.625 * y = 1370
solve for y to get:
y = 1370 / 85.625 = 16.
since the ratio of x to y is 5/8, then you get x = 10.
you have x = 10 and y = 16.
since x * r = 4795, then r must be equal to 4795 / 10 = 479.5
since y * w = 5480, then w must be equal to 5480 / 16 = 342.5
your solution looks like it will be that the cost of a ring is 479.5.
to confirm that the solution is correct, i did the following.
cost of a ring is 479.5
cost of a watch is 342.5
cost of a ring is 137 more than a watch.
342.5 + 137 = 479.5
this part checks out.
total cost of rings is 10 * 479.5 = 4795.
total cost of watches is 16 * 342.5 = 5480.
total cost of both is 4795 + 5480 = 10275.
this part checks out.
the ratio of the number of rings to watches is 5/8.
10/16 = 5/8.
this part checks out.
the ratio of the total cost of rings to total cost of watches is 7/8.
4795/5480 = 7/8.
this part checks out.
all the parts check out, indicating that the solution is correct.
since you were asked for the cost of a ring, then your solution is that the cost of a ring is 479.5.
this solution was only possible when i assumed that the ratio of the number of rings to watches is 5/8 and not that the ratio of the number of watches to rings is 5/8.
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