Answer:
10 girls
11 boys
Step-by-step explanation:
set up a system of equations:
b represents boys, g represents girls
b+g=21 (since there is a total of 21 students)
11b+13g=251 (since each boy has 11 pockets, each girl has 13, total of 251)
i chose the method of substitution, so i solved the first equation to get
b=21-g
then i substitute 21-g for b in the second equation, and solve:
11(21-g)+13g=251
231-11g+13g=251
2g+231=251
2g=20
g=10
then, i solved for boys (by choosing the top equation and substituting 10 for g, since we now know that g=10)
b+g=21
b+10=21
b=11
so there are 10 girls and 11 boys in this class
There are 10 girls and 11 boys in the class.
"It is a statement which consists of equal symbol between two mathematical expressions."
"It is a finite set of equations for which we find a common solution."
For given example,
Let 'x' be the number of girls and 'y' be the number of boys.
Each boy in a class has 11 pockets and each girl in the class has 13 pockets.
And in this class if all 21 students have a total of 251 pockets.
So, we have system of equations,
⇒ x + y =21 .......................(1)
⇒ 13x + 11y = 251 .......................(2)
From equation (1),
x = 21 - y ......................(3)
Substitute this value of 'x' in the equation (2),
⇒ 13(21 - y) + 11y = 251
⇒ 273 - 13y + 11y = 251
⇒ 273 -2y - 273 = 251 - 273
⇒ -2y = -22
⇒ y = -22 / -2
⇒ y = 11
This means, there are 11 boys in the class.
Substitute the value of 'y' in equation (3),
⇒ x = 21 - 11
⇒ x = 10
This means there are 10 girls in the class.
Therefore, there are 10 girls and 11 boys in the class.
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