Answer:
Explanation:
Let's break down the problem step by step.
Step 1: Define your variables.
Let S represent the number of successful candidates, and U represent the number of unsuccessful candidates.
Step 2: Create equations based on the given information.
From the problem statement, we know that "the number of successful candidates was three times that of unsuccessful candidates." This gives us our first equation:
S = 3U
Next, we're told that "if there had been 16 fewer candidates," which means the total number of candidates is S + U - 16. We're also told that "if 6 more would have been unsuccessful," which means the number of unsuccessful candidates would be U + 6. In this scenario, "the numbers would have been as 2 to 1," which gives us our second equation:
(S + U - 16) = 2(U + 6)
Step 3: Solve the equations.
Now, you have a system of two equations:
S = 3U
(S + U - 16) = 2(U + 6)
First, we'll solve equation 1 for S:
S = 3U
Now, substitute this expression for S into equation 2:
(3U + U - 16) = 2(U + 6)
Simplify the equation:
4U - 16 = 2U + 12
Subtract 2U from both sides:
2U - 16 = 12
Add 16 to both sides:
2U = 28
Divide by 2 to solve for U:
U = 14
Now that we have the number of unsuccessful candidates, we can find the number of successful candidates using equation 1:
S = 3U
S = 3 * 14
S = 42
Step 4: Find the total number of candidates.
The total number of candidates is S + U:
Total candidates = 42 + 14 = 56
So, there were 56 candidates in the test.