SOLUTION: In a school,1200 of the students are boys,if 50% of the boys and 40% of the girls have paid their school fees. Find the number of girls,given that 46% of the population have paid t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a school,1200 of the students are boys,if 50% of the boys and 40% of the girls have paid their school fees. Find the number of girls,given that 46% of the population have paid t      Log On


   

Question 1176305: In a school,1200 of the students are boys,if 50% of the boys and 40% of the girls have paid their school fees. Find the number of girls,given that 46% of the population have paid their school fees.
Found 4 solutions by MathLover1, ewatrrr, greenestamps, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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let the number of boys be b and the number of girls be g
given:
b%2Bg=1200
b=1200-g.......eq.1
if 50% of the boys and 40% of the girls have paid their school fees, we have
0.50b+and 0.40g have paid their school fees
if given that 46% of the population have paid their school fees. then
0.46%2A1200=552 have paid their school fees
so
0.50b+%2B0.40g=552........eq.2, substitute b from eq.1
0.50%281200-g%29+%2B0.40g=552
600-0.50g+%2B0.40g=552
600-0.10g+=552
600-552=0.10g+
48=0.10g+
g=48%2F0.10
g=480
b=1200-480.......eq.1
b=720
50% of the boys, which is 0.50%2A720=360 boys, have paid their school fees
and
40% of the girls, which is 0.40%2A480=192 girls, have paid their school fees

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Question States:
 .46(1200) = 552 have paid their school fees.

  .50x + .40(1200-x )= 552
                 x = 72/.10 = 720 boys paid fees and 480 girls have paid.

  360 + 192 = 552  checks.
Wish You the Best in your Studies.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The two solutions you have received so far both use 1200 as the total number of students. The problem says the 1200 is the number of boys....

Let x be the number of girls; then the total number of students is 1200+x.

50% of the boys plus 40% of the girls is equal to 46% of the total number of students:

.50%281200%29%2B.40%28x%29+=+.46%281200%2Bx%29
600%2B.40x+=+552%2B.46x
48+=+.06x
x+=+48%2F.06+=+800

ANSWER: there are 800 girls in the school.

CHECK:
.50(1200)+.40(800) = 600+320 = 920
.46(1200+800) = .46(2000) = 920

Answer by ikleyn(52803) About Me  (Show Source):
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.


            In both posts by  @ewatrrr and  @MathLover1,  everything including the problem setup,  the solution and the answer,
            is  WRONG,  INCORRECT  and  IRRELEVANT,

            because these ladies misread the problem and did not take a labor to read the problem attentively and to understand its meaning.

            I came to bring the correct solution. 


Let x be the number of girls.


Then the total students is  (1200 + x).

The total of those who pays their school fees is  (0.5*1200 + 0.4x) = (600 + 0.4x).


The equation is


    %28600%2B0.4x%29%2F%281200%2Bx%29 = 0.46.


To solve it, multiply both sides by the denominator and simplify


    600 + 0.4x = 0.46*(1200 + x)

    x = %28600-0.46%2A1200%29%2F%280.46-0.4%29 = 800.


ANSWER.  The number of girls in the school is 800.

Solved.