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The equation [tex]$s = 10 - 2h$[/tex] can be used to determine the amount of sugar [tex]$s$[/tex], in teaspoons, that should be added to a tea beverage with [tex]$h$[/tex] teaspoons of honey.

What is the meaning of the 2 in the equation?

A) For every teaspoon of honey in the beverage, two more teaspoons of sugar should be added.
B) For every teaspoon of honey in the beverage, two fewer teaspoons of sugar should be added.
C) For every two teaspoons of honey in the beverage, one more teaspoon of sugar should be added.
D) For every two teaspoons of honey in the beverage, one fewer teaspoon of sugar should be added.

Answer :

To understand the meaning of the number 2 in the equation [tex]\( s = 10 - 2h \)[/tex], let’s break it down:

1. Equation Overview: The equation shows the relationship between the amount of sugar [tex]\( s \)[/tex] and the amount of honey [tex]\( h \)[/tex] in the tea recipe.

2. Identifying Components:
- The [tex]\( 10 \)[/tex] represents a starting amount of sugar in teaspoons before adding any honey.
- The [tex]\(-2h\)[/tex] part of the equation represents the relationship between honey and sugar. Specifically, the negative sign and the number 2 indicate how the amount of sugar changes as you add more honey.

3. Understanding the Role of the Number 2:
- The equation indicates that for each additional teaspoon of honey ([tex]\( h \)[/tex]), you remove 2 teaspoons of sugar ([tex]\( s \)[/tex]). This is because the coefficient of [tex]\( h \)[/tex] is 2 with a negative sign.

4. Conclusion:
- Therefore, the number 2 in the equation means that for every amount of honey (h in teaspoons) added to the tea, you need to reduce the sugar by 2 teaspoons. This interpretation aligns with option B: "For every teaspoon of honey in the beverage, two fewer teaspoons of sugar should be added."

So, the correct answer is:
B) For every teaspoon of honey in the beverage, two fewer teaspoons of sugar should be added.

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