I have a word problem that I am having trouble figuring out. Can someone please help?
When 5 new girls joined a class, the percent of girls increased from 40% to 50. What is the number of boys in the class?
Thank you in advance!
I have a word problem that I am having trouble figuring out. Can someone please help?
When 5 new girls joined a class, the percent of girls increased from 40% to 50. What is the number of boys in the class?
Thank you in advance!
So lets say that girls = g and boys = b
At first it was that: g/(g+b) = 4/10
Which means that: g = (4g+4b)/10
You also know that: (g+5)/(g+b+5) = 5/10
Therefore: g+5 = (5g+5b+25)/10
Subtract: g = (5g+5b+25)/10 - 5
Which means: g = (5g+5b+25-50)/10 = (5g+5b-25)/10
Substitute: (4g+4b)/10 = (5g+5b-25)/10
Multiply both sides by 10 to get: 4g+4b = 5g+5b-25
You can change that into: 25 = g+b
Go back to this: g/(g+b) = 4/10
I hope you understand that: b/(g+b) = 6/10
Substitute: b/25 = 6/10
Multiply both sides by 25 to get: b = 150/10
Simplify: b = 15
So there are 15 boys in the class.
I have a different way to do this problem. it's a bit more complicated than Quick's solution, so if you understand his, just dont bother reading this. in any case, i think its good to think of a problem in more than one way.
Here's the background knowledge you need to follow my method:
you need to know how to solve simultaneous equations. you need to be able to do basic algebra, that is if someone says x + 5 = 7, you should be able to tell me what x is.
Also, recall that "percentage" is just a fancy way of saying "/100", for example, 50% means 50/100 (or 0.5), 40% means 40/100 (or 0.4). also, in math, "of" means multiply, so if someone asks what is 50% of 200, its the same thing as them asking, what does 50/100 * 200 = ?
Now here's the logic. say we had x girls in the class before, and there are y students in total. when 5 new girls join the class, we have x + 5 girls and so we now have y + 5 people in the class. we can now use this information to find y and then we can find how many boys there are. anyway, let's do the problem. The words in red are explanations, so you wouldn't write them on an exam or anything (obviously).
Let the number of girls in the class initially be x.
Let the total class size initially be y.
So we have the simultaneous equations: (do you know how to work with simultaneous equations).
x = 0.4y .............................(1) .......that means the girls in the class originally were 40% of the class (remember, "40% of" means "0.4 * "
x + 5 = 0.5(y + 5) ................(2)
x = 0.4y
x = 0.5(y + 5) - 5 .....................i solved equation (2) for x
now since i have x = something and x = somethign else, it means that something = something else
=> 0.4y = 0.5(y + 5) - 5
=> 0.4y - 0.5y = 5/2 - 5
=> -0.1y = -2.5
=> y = 2.5/0.1 = 25 ............this is the number of students in the class before the 5 additional girls
=> there are now 30 students in the class (since we have 5 additional girls), so the number of boys in the class is 15 (since they now constitute 50%)
simpler solution:
let X be the total original number of students in the class.
number of girls, G = 0.40 X
Number of boys, B = 0.60 X
(G+5)/(X+5)=.50
(0.40 X+5)/(X+5)=50/100
X+5=0.8X+10 ======> X=25
Therefore, the total number of students =25
G=0.40*25=10
B=0.60*25=15
total 25 (check ==> 10/25=0.40, 15/25=0.60 ===> OK)
After the addition of 5 girls ...
G=10+5=15
B=15
total 30 (check ==> 15/30=0.50 ===> OK)
Hello, DJ13!
I used a different approach . . .
When 5 new girls joined a class, the percent of girls increased from 40% to 50%.
What is the number of boys in the class?
Let $\displaystyle C$ = number of students in the class (originally).
The class was 40% girls: .The number of girls was: $\displaystyle 0.40C$
Five girls joined the class; there are $\displaystyle 0.40C + 5$ girls.
. . But this is 50% of the enlarged class .. which has $\displaystyle C + 5$ students.
Hence, we have: .$\displaystyle 0.40C + 5 \:=\:0.50(C + 5)$
. . . . . . . . . . . . .$\displaystyle 0.40S + 5 \:=\:0.50C + 2.5$
. . . . . . . . . . . . . . $\displaystyle \text{-}0.10C \:=\:\text{-}2.5$
. . . . . . . . . . . . . . . . . $\displaystyle C \:=\:25$
The original class had 25 students.
And 60% of them were boys: .$\displaystyle 0.60 \times 25 \:=\:\boxed{15\text{ boys}}$