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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.
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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