Question 1177050
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.