Question 4

The value of x is 53.

To solve the equation (70% of 32.5) + (25% of x) = 36, we first calculate 70% of 32.5, which equals 22.75. Subtracting this from 36 gives us 13.25, and since 25% of x equals 13.25, we find that x must be 53.

A) 45

The value of 45 is incorrect because if we calculate 25% of 45, we get 11.25. Adding this to 22.75 results in only 33.50, which does not satisfy the equation since we need the total to equal 36.

B) 53

This option is correct because 25% of 53 equals 13.25. When we add this to 22.75 (which is 70% of 32.5), the total equals 36, fulfilling the requirement of the equation.

C) 78

The value of 78 is incorrect because 25% of 78 equals 19.5. Adding this to 22.75 results in 42.25, which exceeds the needed total of 36.

D) 135

The value of 135 is incorrect as 25% of 135 equals 33.75. When combined with 22.75, the total becomes 56.50, which is also greater than 36.

E) 161

The value of 161 is incorrect because 25% of 161 equals 40.25. Adding this to 22.75 results in 63, which far exceeds the target total of 36.

Conclusion

The correct answer is 53 because it is the only value that, when calculated with 25%, results in the correct total of 36 when added to 70% of 32.5. All other options fail to meet the equation's requirement, either falling short or exceeding the necessary total.