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Let's say the number of girls is x and the number of boys is y. Then the information we have is:

There are 51 students, so: x + y = 51

And 12 less than twice the number of girls are boys, so: y = 2x-12

Replace y in the first equation with the second and you get:

x + (2x-12) = 51

3x = 63

x = 21

So there are 21 girls in the ninth grade. To check back, that means there should be 30 boys, and that is indeed 12 less than twice the number of girls.

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Q: The number of boys in the ninth grade is 12 less than twice the number of girls there are 51 students in the ninth grade how many are girls?
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Let's lay out the known information in equations, where B is the number of boys and G is the number of girls. Then we express the number B in terms of G, which is twice as much less 12, or (2G-12) B + G = 51 , and B = 2G - 12 Now, replace the B in the first equation with its value from the second equation (2G - 12) + G = 51 Remove the brackets 2G - 12 + G = 51 Add 12 to both sides 2G + G = 51 + 12 3G = 63 Divide both sides by 3 G = 21 Now, to check if we're right, Replace G in the first equation B + 21 = 51 B = 30 If that's right then 30 = 2(21) - 12 30 = 42 - 12 And it is, so we know that there are 21 girls and 30 boys in ninth grade.


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