Final answer:
After setting up and solving two separate proportions, it is found that the value of x that satisfies the ratios 2:3 to 2:x is x = 3, and the value that satisfies the ratios 18:39 to x:54 is x = 24.9. Since these values of x are not equivalent, there is no value of x that makes both given ratios equivalent.
Step-by-step explanation:
To find the value of x so that the ratios 2:3 to 2:x and 18:39 to x:54 are equivalent, we need to set up two separate proportions and solve for x. For the first proportion, we have 2:3 = 2:x, which simplifies into 2x = 6 when we cross multiply, giving us x = 3.
For the second proportion, we have 18:39 = x:54. Cross multiplying gives us 18 * 54 = 39x, which simplifies to 972 = 39x. Solving for x, we divide both sides by 39 to get x = 24.9. However, since x needs to satisfy both proportions, and the first proportion concluded x = 3, there's no single value of x that makes both proportions equivalent, as 3 is not equal to 24.9.
Therefore, there is no value of x that makes both ratios equivalent.