Question 180041: I know the answer to my question, because I kept multiplying, but I don't know howto show my work as a stratey. The question is. In a math class of 26 students, each girl drew a triangle and each boy drew a rectangle. There were 92 slides in all. How may girls and how many boys were in the class. The answer I came up with was 16 girls and 11 boys.
Found 3 solutions by nerdybill, scott8148, Earlsdon:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! There are 3 sides to a triangle and 4 sides to a rectangle.
Let g = number of girls
and b = number of boys
then since we have two variables, we'll need two equations.
.
g + b = 26 (equation 1)
3g + 4b = 92 (equation 2)
.
solving equation 1 for g, we get:
g = 26-b
.
Substituting the above into equation 2 we can then solve for b:
3g + 4b = 92
3(26-b) + 4b = 92
78 - 3b + 4b = 92
78 + b = 92
b = 14 (number of boys)
.
Substitute the above into equation 1 and solve for g:
g + b = 26
g + 14 = 26
g = 12 (number of girls)
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! 16 + 11 = 27 ... not 26
let g=girls and b=boys
"a math class of 26 students" __ g + b = 26 __ g = 26 - b
"each girl drew a triangle and each boy drew a rectangle. There were 92 slides in all"
__ I'm thinking "sides", not slides...
__ 3g + 4b = 92
substituting __ 3(26-b) + 4b = 92 __ 78 - 3b + 4b = 92
subtracting 78 __ b = 14
substituting __ g + (14) = 26
subtracting 14 __ g = 12
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! Let B = the number of boys and G = the number of girls.
B+G = 26 "The number of students is 26"
The girls drew triangles, each of which has three sides, so the total number of sides from the triangles is: 3*G
The boys drew rectangles each of which has four sides, so the total number of sides from the rectangles is: 4*B
Now you can write two equations as follows:
1) B+G = 26 Rewrite this as: B = 26-G and substitute for B in equation 2).
2) 4*B+3*G = 92 which is the total number of sides.
4(26-G)+3*G = 92 Simplify and solve for G.
104-4G+3G = 92 Subtract 104 from both sides.
-G = -12 Divide through by -1 to make positive.
G = 12
To find the number of boys (B):
B = 26-G
B = 26-12
B = 14
So the number of boys is 14 and the number of girls is 12
Check:
B+G = 26
14+12 = 26
26 = 26 OK!
4*B+3*G = 92
4*14+3*12 = 92
56+36 = 92
92 = 92 OK!
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