Maths SOS!!?

Question

Heres the thing.
I am baby sitting my 13 year old neice,as well as giving her tution.But there are some questions which she faced difficulty and even i could not slove.
Heres the two questions:
John bought 12 boxes of mango at $60 and each box contains x mangoes.15% of it was rotten and could not be sold.If he sells it for 25 cents each,he would make a profit of 70%,find the number of mangoes in each box.

Second Question:
A club comprising of boys and girls has a total of 160 members.If 32 more girls join the club,the percentage of girls will increase by 5%.How many boys are there in the club?

Please help as i have tried sloving the questions but to no avail.(and my neice is getting anxious)

Thanks!(please include working for the questions)

Answer 1

OK..Easy! Best to work backwards on PROBLEM #1. So, if John made a 70% profit, after originally spending $60, that would mean he NOW has: $102 [60 x 1.70 = 102] so: If he was selling mangoes at 25 cents each, he would have to had sold 408 mangoes to make $102 [102 / 0.25 = 408] NOW: if he had 408 GOOD mangoes to sell, (after having lost 15% to rot), that means 85% (100% - 15% ) of a certain number, x, equals 408....or, expressed algabraically:.. 0.85x = 408..... therefore x = 408/0.85.. or 480....So, this means he ORIGINALLY had 480 mangoes. Finally, if there were 12 boxes and 480 mangoes total, there would be 40 mangoes in each box [480 divided by 12 = 40] SO: The answer to your first question is 40 mangoes in each box, BEFORE losing the rotten ones........so, after he lost 15% there would be only 34 mangoes in each box. PROBLEM #2 Let x = the number of girls. Therefore, x/160 is the original % of girls. If we add 32 girls, the # of girls is now x + 32 and the new total of students is 160 + 32 or, 192,.....and the NEW percentage of girls is represented as: (x + 32) / 192 and the increase of 5% is represented as: (x /160) + .05 All of this can be represented algabraically as: (x +32) / 192 = (x / 160) + .05 Multiply both sides of the equation by 192 to get: x + 32 = (192x/160) + 9.6 Then simplify the equation further by multiplying each value by 160 to get: (160x + 5120 = 192x + 1536) Further simplifying: 32x = 3584 Therefore: x = 112 So, the original # of girls is 112. Therefore 112 girls out of a total of 160 students = 70% (112/160 = 70%) Increase the girls by 32, you have 144 girls and a new total of 160+32 Therefore: 144/192 = 75% for your increase of 5% which proves the solution. Don't forget though!! The question was: HOW MANY BOYS? Of course the answer is 48. (160 minus 112) (Most math teachers are VERY fussy! They want an answer to their question!!)

Answer 2

Second question first:

Let x and y be the number of boys and girls and so a + b = 160. Adding 32 more girls makes the percentage of the girls increase by 5%

[(b + 32) / 192 - b / 160) ] x 100 = 5

b/192 + 32/192 - b/160 = 5/100 = 1/20

b/192 - b/160 = 1/20 - 1/6

160 b - 192 b = 192 x 160 x (3 - 10) / 60 = -7 x 192 x 160 /60

- 32b = - 7 x 192 x 160 / 60

So negative sign can be canceled.

b = 7 x 192 x 160 / (60 x 32)

= 112

So the number of boys is 160 - 112 = 48

Let us verify the results.

Percentage of girls originally = 100x 112/160 = 70

Percentage after 32 more girls join = 100 x 144 / 192 = 75

So, our calculation is correct.

Now let us try the first question:

12 boxes contain 12 x mangoes.

15% of them got spoilt. So, remaining mangoes are 0.85 x 12 x

They were sold at 25 cents each and the resultant amount is 70% more than 60 dollars, the price John paid.

So, 0.85 x 12 x 0.25 x = 1.7 x 60

2.55 x = 102

x = 102/2.55 = 40



So each box had 40 mangoes.

Answer 3

Here is the solution for the second one:

THe equation you need to solve is this:

(g+32)/(160+32)=(g/160)+.05

The left side represents the percentage of girls when the 32 are added, and the right side tells is equal to it because it is the old percentage plus the 5%.

At this point it is simple algebra, the answer is g=112, or 112 girls, so there are 48 boys in the class.

Answer 4

Solution Provider: Eroz Awari (S.G.M.Shiroiya School, navsari)
Second Question Solution:

Let the number of boys be = x
& the number of girls be = y

Now, From the given data we can form a given below equation:

x + y = 160 -----------------------------Eq.No 1.
y = 160 - x (by applying the algebric rules:)


Now, if 32 more girls join the club, the percentage of girls will increase by 5%. this statement can be mathematically depicted by:

y + 32 = (160 - x) + (160 -x)*5/100
y+32 = (160 -x) + (160 - x)/20
y+32 = [20(160-x) + 160 - x)] /20
20 ( y + 32) = 3200 - 20 x + 160 - x
20y + 640 = 3360 - 21x
21x + 20y = 3360 - 640
21x + 20y = 2720 ----------------------->Eq No 2.

Now, Solve Eq. No 1 & 2
and U will get the answer.

Answer 5

let,the no.of girls=x;then,the no. of boys would be=160-x,
the percentage of girls=5x/8

after adding 32 girls--
the total no.of members=160+32=192
total no. of girls=x+32
percentage of girls now=100(x+32)/192

according to the question-
the percentage has been increased by 5%
so,(5x/8)+5=100(32+x)/192
x=112

the no. of boys=160-112=48

i tried my level best,check the answer and let me know that whether its ok or not.the another question is already solved so i didn't try it,if need it also let me know i will solve it for you,byeeeeeeeeeeeeeeeeee,thanks

Answer 6

he number of mangos he will sell is 0.85 * 12 *x
he will sell them 0.25 dollar each
so he will get 0.25 *0.85 *12 x dollars = 2.55 x
70% profit =60*70/100 = 42
so he will get 42+60 =102 $
so
2.55 x =102
x= 102/2.55 = 40
---------------------------
(g+32)/192 - g/160=.05
160g +32*160 - 192g =0.5*160*192 =1536
-32g + 5120 =1536
32g =5120-1536 = 3584
g=112
b=160-112= 48
so there are 48 boys

Answer 7

12x = $60
12x (.85) x .25 = $60 x 1.7 (70 % profit)
2.55x = 10200 ($102.00)
40 mangoes in a box
****************
5% = 32
can't be - even at 100% girls - a 5% increase would be 8

something is wrong in the problem

Answer 8

whilst that's in parenthesis it contains the two the "-" and the "2". so which you have: (-2)^4 = -2 x -2 x -2 x -2 = sixteen (because of the fact 2 negatives become a helpful whilst it isn't any longer in parenthesis it only contains the variety raised to the flexibility of four so which you have -2^4 = -a million x 2 x 2 x 2 x 2 = -a million x sixteen keep in mind that the -2 is referred to as -a million x 2 because of the fact something circumstances a million is itself