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Josephine is taking a college course, and her professor bases the course grade on the average of 2 tests taken in the semester. She wants to know what she needs to earn on the last test to maintain her grade.

Rearrange the following equation for [tex]\( b \)[/tex], where [tex]\( C \)[/tex] is the average of 2 test scores, [tex]\( a \)[/tex] and [tex]\( b \)[/tex].

[tex]\[ C = \frac{a + b}{2} \][/tex]

A. [tex]\( b = \frac{2C}{a} \)[/tex]
B. [tex]\( b = 2C + a \)[/tex]
C. [tex]\( b = 2C - a \)[/tex]
D. [tex]\( b = 2C(a) \)[/tex]

Sagot :

GinnyAnswer
To solve for [tex]\( b \)[/tex] in the equation [tex]\( C = \frac{a + b}{2} \)[/tex], we need to rearrange the equation step-by-step.

1. Start with the given equation:
[tex]\[ C = \frac{a + b}{2} \][/tex]

2. To eliminate the fraction, multiply both sides of the equation by 2:
[tex]\[ 2C = a + b \][/tex]

3. Next, isolate [tex]\( b \)[/tex] by subtracting [tex]\( a \)[/tex] from both sides:
[tex]\[ 2C - a = b \][/tex]

So, the rearranged equation solving for [tex]\( b \)[/tex] is:
[tex]\[ b = 2C - a \][/tex]

This matches one of the provided options:
[tex]\[ b = 2C - a \][/tex]

Thus, the correct answer is:
[tex]\[ b = 2C - a \][/tex]
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