Final answer:
Upon solving the equation ({8}/{15} + {3}/{10} + {3}/{5} = {13}/{x}), it is found that x = 390 / 43, which is approximately 9.07. This does not match any of the given options, indicating there might be an error in the equation or the solution process.
Step-by-step explanation:
To solve for x in the equation ( {8}/{15} + {3}/{10} + {3}/{5} = {13}/{x} ), first, we need to find a common denominator for the fractions on the left side of the equation. The least common denominator (LCD) for 15, 10, and 5 is 30. Now we convert each fraction to an equivalent fraction with the denominator of 30:
- {8}/{15} becomes {16}/{30}
- {3}/{10} becomes {9}/{30}
- {3}/{5} becomes {18}/{30}
Adding these fractions gives us {16}/{30} + {9}/{30} + {18}/{30} = {43}/{30}. Now, we equate the sum of these fractions to {13}/{x}:
{43}/{30} = {13}/{x}
To find the value of x, we can cross-multiply:
43x = 13 × 30
43x = 390
Dividing both sides of the equation by 43 to isolate x, we get:
x = 390 / 43
x = 9.0697 (approx.) which is not one of the options provided. However, rechecking the addition, we realize it should be {43}/{30} = {13}/{x}. By comparing, we see that 43/13 = 30/x.
Now we cross-multiply:
43 × x = 13 × 30
x = (13 × 30) / 43
So:
x = 390 / 43
x = 9.07 (approx.)
There seems to be an error, as none of the options provided (a) 30 (b) 20 (c) 10 (d) 15 match the value obtained. The student should recheck the original equation or the solution steps.