A total of 348 teachers are attending a conference. Suppose 195 of those attending are math teachers, and the other attendees are science teachers (x). Which THREE statements are correct for this situation?

Question

Responses
A 195x = 348195x = 348
B x + 195 = 348x + 195 = 348
C x = 348 − 195x = 348 − 195
D 153 science teachers attend.153 science teachers attend.
E 161 science teachers attend.

Answer 1

To analyze the situation, we know that there are a total of 348 teachers, with 195 being math teachers. The number of science teachers can be represented as \( x \).

We can derive the following relationships from the information given:

1. The total number of teachers is the sum of math teachers and science teachers: \[ x + 195 = 348 \]

2. We can also express the number of science teachers in another way: \[ x = 348 - 195 \]

Now, let's evaluate the statements:

A. \( 195x = 348 \)

• This is incorrect because it wrongly implies a multiplication relationship rather than addition.

B. \( x + 195 = 348 \)

• This is correct, reflecting the total number of teachers.

C. \( x = 348 - 195 \)

• This is also correct, as it rearranges the equation to solve for \( x \).

D. 153 science teachers attend.

• This is incorrect. If we calculate \( x \) using \( x = 348 - 195 \): \[ x = 348 - 195 = 153, \] while this calculation is correct, the statement is put in a numerical form that suggests a truthful numerical representation.

E. 161 science teachers attend.

• This is incorrect according to our calculations.

Thus, the correct statements are:

• B. \( x + 195 = 348 \)
• C. \( x = 348 - 195 \)
• D. 153 science teachers attend. (This calculation is valid and matches the result from \( x = 153 \))

In summary, the correct statements are B, C, and D.