To determine which sentence accurately describes the equation [tex]\( 105 = 78 + y \)[/tex], let's break down what the equation means step by step.
1. We start with the equation: [tex]\( 105 = 78 + y \)[/tex].
2. This equation indicates that when 78 is added to some unknown number [tex]\( y \)[/tex], the result equals 105.
Given the options, we need to find the one that correctly describes this relationship:
1. The sum of 78 and a number is 105. \
This sentence states that when you add 78 to another number, the result is 105. This is consistent with the equation [tex]\( 105 = 78 + y \)[/tex], where 78 plus [tex]\( y \)[/tex] equals 105.
2. The number 105 is more than 78. \
This sentence simply states that 105 is greater than 78, but it doesn't capture the relationship described by the equation.
3. The sum of 105 and 78 is a number. \
This sentence describes adding 105 and 78 together, which is not what the equation shows. The equation shows that adding 78 to some number [tex]\( y \)[/tex] will result in 105, not the sum of 105 and 78.
4. Seventy-eight is more than the number one hundred five. \
This sentence is incorrect because 78 is actually less than 105.
Based on this analysis, the first sentence accurately describes the equation [tex]\( 105 = 78 + y \)[/tex]:
The sum of 78 and a number is 105.
Thus, the correct choice is: The sum of 78 and a number is 105.
