Which of the following expressions represents the sum of three × a number and eight × another number?

Rationale

3x + 8y is the expression that represents the sum of three times a number and eight times another number.

This algebraic expression shows the sum of two different numbers, each multiplied by a separate coefficient. Here, 'x' and 'y' are placeholders for the two different numbers, while '3' and '8' are the multipliers. The '+' operator signifies the operation of addition between the two terms.

A (3x + 8x) YOUR ANSWER

This expression represents the sum of three times a number and eight times the same number, not another number. In this case, 'x' is used for both numbers, which means the numbers are the same. This is not the intended scenario as per the question.

B (3x + 8y) CORRECT

This expression accurately represents the sum of three times a number 'x' and eight times another number 'y'. The use of different variables ('x' and 'y') indicates that the numbers are different, as required by the question.

C (8x - 3y) YOUR ANSWER

This expression represents the difference between eight times a number and three times another number, not the sum. The '-' operator signifies the operation of subtraction, not addition.

D (3x - 8y) YOUR ANSWER

This expression represents the difference between three times a number and eight times another number, not the sum. Again, the '-' operator signifies the operation of subtraction, not addition.

Conclusion

The expression '3x + 8y' correctly represents the sum of three times a number and eight times another number. '3x + 8x' represents the sum of three times a number and eight times the same number, not a different one. '8x - 3y' and '3x - 8y' both represent the difference between multiples of two numbers, not the sum. Therefore, the correct answer is '3x + 8y'.

Which of the following expressions represents the sum of three × a number and eight × another number?

3x + 8y is the expression that represents the sum of three times a number and eight times another number.

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