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2 years ago

the ratio of boys to girls in janices classroom is 3:5, and there are a total of 32 students in the class, help plss

Mathematics

1 answer:

svetoff [14.1K]2 years ago

5 0

9514 1404 393

Answer:

12 boys
20 girls

Step-by-step explanation:

The total number of students (32) corresponds to the total number of ratio units (3+5 = 8), so each ratio unit represents 32/8 = 4 students.

The 3 ratio units representing boys will stand for 3×4 = 12 boys.

The 5 ratio units representing girls will stand for 5×4 = 20 girls.

There are 12 boys and 20 girls in Janice's classroom.

_____

<em>Additional comment</em>

I find the above solution to be the easiest.

You can also write a system of equations. Let b and g represent the numbers of boys and girls, respectively.

b/g = 3/5

b +g = 32

Multiplying the first equation by g gives an expression for b that can be substituted into the second equation:

b = (3/5)g

(3/5)g +g = 32

8/5g = 32 . . . . . . . . . . . . . . . . . collect terms

g = (5/8)(32) = 5·4 = 20 . . . . . . multiply by 5/8

b = (3/5)(20) = 3·4 = 12 . . . . . . . find b using the value of g

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Morgarella [4.7K]

Hello from MrBillDoesMath!

Answer:

33769/181

Discussion:

Each term contains "x" so factoring it out gives

x( 1/4 + 1/14 + 1/17) = 71 (*)

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3 years ago

Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none

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Answer: The required solution of the given system is

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$x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (i), we have

$x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii), we get

$y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.$

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$y=4-3=1.$

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$y=4-4=0.$

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8 0

3 years ago

the ratio of boys to girls in janices classroom is 3:5, and there are a total of 32 students in the class, help plss​

the ratio of boys to girls in janices classroom is 3:5, and there are a total of 32 students in the class, help plss