theres this easy question "A math club has 12 boys and 8 girls. Every week, the membership increases by 2 girls and one boy. When there are as many boys as girls(when theyre the same), the total number of club members is .....four options are 40,32,24,16 i know of course that its 32....but the question says (use algebra equation)...can someone form the equation for me( u have to let x represent the number of weeks in the equation)
2007-01-05 02:33:10 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
the initial boys=12 increase per week=1
so in 'n' weeks=12+n
initial girls=8
increase per week=2
so in 'n' weeks=8+2n
equating and solving
12+n=8+2n
n=4 weeks
so boys=16 and girls=16 total=32
2007-01-05 02:40:03 · answer #1 · answered by raj 7 · 2⤊ 0⤋
We start out with 12 boys, each week we get 1 more, so by the nth week, we have 12 + n. (n = number of weeks)
We start out with 8 girls and each week we get 2, so by the nth week, we have 8 + 2n.
They want to know how many people are in the club when the number of girls equals the number of boys. Let's figure out how many weeks it takes for the number to be equal:
12 + n = 8 + 2n
12 + n - 8 = 8 + 2n - 8
4 + n = 2n
4 + n - n = 2n - n
n = 4 weeks.
It will take 4 weeks for the two to be equal (double check this by figuring out how many boys there will be in 4 weeks and how many girls there will be in 4 weeks and making sure they're equal).
So this means that in 4 weeks, there will be a total of [12 + 4] + [8 + (2 x 4)] = 16 + 16 = 32 people in the club when there are the same number of boys and girls.
2007-01-05 10:59:56 · answer #2 · answered by Wendy C 2 · 0⤊ 0⤋
after x weeks, the number of boys is : 12 + x
the number of girls is 8 + 2*x
thus the total number of members is 20 + 3*x
When there are as many boys as girls 12+x = 8+2*x
=> x = 4
then the total number is 20 + 3*4 = 12
2007-01-05 10:52:48 · answer #3 · answered by James Chan 4 · 0⤊ 0⤋
Each week the number of members increase:
boys = 12 + x
girls = 8 + 2*x
You want to know when the amount of boys equals the amount of girls (boys = girls)
12+x = 8 + 2*x
Move x to one side, and numbers to the other side:
12-8 = 2*x-x
4 = x
x = 4
Four weeks later, there are 12 + x boys, and 8 + 2*x girls:
12+x = 12+4 = 16
8 + 2*4 = 8+8 = 16
You can add (12+x) and (8+2*x):
x+12
2x+8
------- +
3x+20
Check: 3*4 + 20 = 12+20 = 32
Write down the formulas just like your teacher wants you to.
2007-01-05 10:43:40 · answer #4 · answered by Anonymous · 5⤊ 0⤋