Generate an image of an antique wooden table with an old-fashioned gold-rimmed ceramic mug of coffee next to it. On the table, arrange three different sizes of money stacks denoted with cardboard cutout figures standing next to each stack. The largest stack is for 'X', the medium stack for 'Y', and the smallest stack for 'Z'. The stacks should be proportional to the ratio of 10:7:5. A subtle clue in the image could be a carefully placed pebble, signifying that Y gets slightly more than Z. Keep the image neutral-toned to emphasize the theme of mathematics and allocations.

A sum of money is divided among three persons, X,Y and z in the ratio of 10:7:5. if Y gets $14 more then Z, how much X will get and what is the total sum of money?

>10 + 7 + 5 = 22

thus there are 22 shares.
let A be the total money.
> X = (10/22)A
> Y = (7/22)A
> Z = (5/22)A
Given That:
> Y = Z + 14
> (7/22)A = (5/22)A + 14
> (7/22)A - (5/22)A = 14
> (2/22)A = 14
> A = (22/2)14
> A = 154
total amount is $154.00
> X = (10/22)A
> X = (10/22)(154)
> X = 70
X gets $70.00

x/y = 10/7

y/z = 7/5
y = z+14

if a/b 1/3 b/c 2/5 then find a/c

To find how much X will get, we need to first find the ratio of the amounts received by Y and Z.

The given ratio of X:Y:Z is 10:7:5.

Let's assume that the common ratio is represented by 'k'. So, we have:

X = 10k
Y = 7k
Z = 5k

It is given that Y gets $14 more than Z. So, we can set up the equation:

7k = 5k + $14

Now, let's solve this equation to find the value of 'k':

7k - 5k = $14
2k = $14
k = $7

Now that we have the value of 'k', we can substitute it back into the expressions for X, Y, and Z to find their respective amounts:

X = 10k = 10 * $7 = $70
Y = 7k = 7 * $7 = $49
Z = 5k = 5 * $7 = $35

So, X will get $70.

To find the total sum of money, we can add up the amounts received by all three persons:

Total sum = X + Y + Z = $70 + $49 + $35 = $154

Therefore, the total sum of money is $154.

154

To find the value of a/c, we need to find a common ratio between a, b, and c.

Since a/b = 1/3 and b/c = 2/5, we can multiply these ratios to find a common ratio:

(a/b) * (b/c) = (1/3) * (2/5)
a/bc = 2/15

Now we can isolate a/c by multiplying both sides of the equation by c:

(a/bc) * c = (2/15) * c
a = (2c)/15

Therefore, the value of a/c is (2c)/15.

Well, isn't this interesting! So, if we take the ratio of 10:7:5 and assume that Z gets $x, then Y would get $x + $14.

Now, we can set up an equation. Since the sum of money is divided among X, Y, and Z, the total sum of money would be 10x + 7(x+14) + 5x.

Simplifying that equation gives us 10x + 7x + 98 + 5x, or 22x + 98.

So, the total sum of money is 22x + 98. As for the amount X will get, it would be 10x.

Unfortunately, without knowing the value of x, I can't give you specific numbers. But hey, at least you've got the equations sorted!