Question 1

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

This expression correctly captures the requirement of summing three times one variable and eight times another variable, where 'x' represents the first number and 'y' represents the second number.

A) 3x + 8x

This expression represents the sum of three times one number and eight times the same number, which simplifies to 11x. However, it does not account for two different numbers, which the question specifies.

B) 3x + 8y

This expression accurately represents the sum of three times one number (3x) and eight times another number (8y). It reflects the relationship described in the question perfectly.

C) 8x - 3y

This option indicates eight times one number minus three times another number. The use of subtraction is incorrect as the question specifically asks for a sum, making this expression unsuitable.

D) 3x - 8y

Similar to option C, this expression suggests three times one number minus eight times another number. Again, this does not match the requirement for a sum, rendering it incorrect.

Conclusion

The expression 3x + 8y is the only one that correctly represents the sum of three times one number and eight times another number. All other options either misinterpret the relationship by using subtraction or incorrectly combine the same variables, failing to adhere to the original question's requirements.