Fruit Basket

a=apples, m=mangoes, o=oranges. If all apples except 4, this means o+m=4 eq.1 If all oranges except 5, this means a+m=5 eq.2 If all mangoes except 7, this means o+a=7 eq. 3

Solve this simultaneous equations. a=1, m=4, o=3 So total number of fruits is 8

a= apples, b=mangoes, c=oranges.. z=total fruits

(1) z-4=a

(2) z-5=b

(3) z-7=c

Adding the 3 equations,

3z-16= a+b+c

3z-16= z

z=8

apples+4=TOTAL_FRUITS ----1

oranges+5=TOTAL_FRUITS -----2

mangoes+7=TOTAL_FRUITS ----3

TOTAL_FRUITS=apples+oranges+mangoes=x

NOW adding up equations

apples+oranges+mangoes+16=TOTAL FRUITS+TOTAL FRUITS+TOTAL_FRUITS

apples+oranges+mangoes+16=3(TOTAL_FRUITS)

x+16=3x

sending x to RHS

16=2x

x=16/2

ie...
x=8

Anybody else kind of winged it without really using equation? I added up everything first but realized I made a mistake. Then I had a thought. What if mango was one. That leaves seven remaining. Then I thought, with one mango, you subtract one from the all but remaining (so 4 and 5) giving you 3 and 4. So that gives you eight total. Didn't really pen and paper it, just thought out loud to myself.

oranges+mangoes=4
mangoes+apples=5 apples+oranges=7

=> 2(O+M+A)=16 which means total number of fruits will be 8

let n=total no. of fruits now n-4=apples,,,,,,n-5=oranges,,,,,,,,,,,n-7=mangoes
as it contains only these fruits their algebric sum must be equal to total fruits that are =n so n-4+n-5+n-7=n 3n-16=n 3n-n=16 2n=16 n=8

ans is 8

Every fruit is counted twice..so add and divide by 2

[o+m]+[a+m]+[a+o]=4+5+7

2[a+o+m]=16

a+o+m=8

a-(o+m) =>a-4 =>a=4,
o-(a+m) =>o-5 =>o=3,
m-(a+o) =>m-7 =>m=1,
Total 8 fruits

a+o=7 a+m=5 o+m=4
a+m-(o+m)=1 a-o=1 a-o+a+o=8 2a=8 a=4 sub a in to equations and solve the rest. a=4,m=1,o=3

let's denote : $A = apple, O = orange, M = mango$ .

let: $A+O+M = X$ given from the question, $A = X - 4, O = X-5, M = X-7$

by adding those 3 equations we get: $3X-16 = X \Rightarrow \boxed{X = 8 }$

(4+5+7)/2=8 fruits in the basket

Let apples be A, mangoes be M, oranges be O. So we have to find A+M+O. Now from given condition, A+M+O - (A)=4. So, M+O=4.........(1) . Similarly, A+M=5..........(2) A+O=7............(3) Therefore, adding (1),(2),(3), M+O+A+M+A+O=4+5+7 2(M+O+A)=16 So, (M+O+A)=8 So, there are 8 fruits in the basket .

a = n of fruits

ap = n of apples

o = n of oranges

m = n of mangos

a - ap = 4

a - o = 5

a - m = 7

3a - (ap + o + m) = (4 + 5 + 7)

3a - a = 16

2a = 16

a = 16/2 = 8

and ap = a - 4 =8 - 4 = 4

and o = a - 5 = 8 - 5 = 3

and m = a - 7 = 8 - 7 = 1

Let the total no. of fruits = F, that of apples, oranges, mangoes be a, o, m respectively. Therefore a + o + m = F

According to the conditions given: Condition 1: no. of all fruits other than apples = F - a = 4 Condition 2: no. of all fruits other than oranges = F - o = 5 Condition 3: no. of all fruits other than mangoes = F - m = 7

Adding all of the above, we get: -> 3F - (a + o + m) = 4 + 5 + 7 -> 2F = 16 -> F = 8

Hence, total no. of fruits = 8

$o+m=4$

$a+m=5$

$a+o=7$

$\therefore a+m+o=8$

orange:a mango:b apple:c we have 3 equations and 3 unknown subjects

a + b =4

b + c =5

a + c =7

solve it we have a=3, b=1, c=4. so the answer is 8

Well, let's suppose we have x fruits. Apples are x-4. Oranges are x-5. Mangos are x-7. So, (x-4)+(x-5)+(x-7) = x 3x - 16 = x 2x = 16 x=8

let the total number of fruits in the basket be x, then there are x-4 apples,x-5 oranges, x-7mangoes, now since the only fruits in the basket are apples , mangoes and oranges, so (x-4) + (x-5) + (x-7) = x therefore x = 8

x=all fruits x-4=apples; x-5=oranges; x-7=mangoes All except 4 are apples meaning 4 is composed of oranges and mangoes. 4=x-5+x-7 which equals to 4=2x-12 All except 5 are oranges meaning 5 is composed of apples and mangoes. 5=x-4+x-7 which equals to 5=2x-11

subtraction of equalities: 4=2x-12 --- 20=10x-60; 5=2x-12 --- 20= 8x- 44 balance: 0 =-2x+16 transposition:2x= 16 answer: x=8

apples=x-4,oranges=x-5,mangoes=x-7, sum of all these terms must be x, said the sherlock holmes

Let, there are x fruits in the basket. So, Apple is = x- 4; Orange is = x-5; Mango is = x-7; So, x-4+x-5+x-7 = x or, x=8 So, there are total 8 fruits in the basket Ans. 8

[mango]+[apple] = 5 [apple]+[orange]= 7 [orange]+[mango]= 4

Distribution isn't an opinion, so [mango] has the smallest value (they are in both low-cardinal-number combinations). [apple]+[orange] can be made neither of 5 and 2, nor of of 6 and 1. Therefore it's made up of 3 and 4. Use [mango] as discriminant and you get it.

(eq1) 7 = o+a (eq2) 5 = m+a, (eq3) 4 = m+o ------> presto!

4= Laranja+ Manga 5=Manga+Maça 7=Maça+Laranja 16=2 Laranjas +2 Maças +2 Mangas/2= 8

نفرض ان الاجمالى = t نرمزللتفاح برمز a نرمز للبرتقال بالرمز o نرمز للمانجو بالرمز m t=a+o+m a=t-4 o=t-5 m=t-7 t=t-4+t-5+t-7 t=3t-16 t-3t=-16 -2t=-16 t=8 اذا مجموع الفاكهة فى الباسكت =8

1) a+o=7 2)a+m=5 3)o+m=4 solving these equations two at a time ,we get a=4, o=3 and m=1<total fruits=8

All the fruit are Apples, except four. That means those four contain oranges + mangoes. We know that there are more oranges than mangoes, so it has to be three oranges, 1 mango. All the fruit are oranges EXCEPT 5 OF THEM. One of those five is a mango, which means there are 4 apples. We can check if it's correct because of 'all of them are mangoes except 7 of them'. 3 oranges + 4 apples = 7 fruit that are not mangoes. 3 oranges + 4 apples +1 mango = 8 fruits in total.

Let total fruits be x. Then Apples = x-4, oranges = x-5, mangoes =x-7, The sum of these should be equal total no of fruits.. So (x-4)+(x-5)+(x-7)=x; 3x-16=x; So x=8 ans....

Let "x","y","z" be no. of apples, oranges, mangoes respectively. According given conditions we gwt 3 equations,......... y+z=4;........x+z=5;......x+y=7;.....On solving we get x=4,........y=3,..........z=1.........hence total fruit is x+y+z=8.

A=apple O=orange M=mango

and F=all fruit

so F=A+O+M and A=F-4 O=F-5 M=F-7

F=F-4+F-5+F-7

3F-F=16 2F=16

and the answer is F=8

a = apples, m = mangoes, o = oranges So,we have to find a + m + o = ???? as per the info : If all apples except 4, this means o+m=4 eq.1 If all oranges except 5, this means a+m=5 eq.2 If all mangoes except 7, this means o+a=7 eq. 3

Therefore, (o + m) + (a + m) + (o + a) = 4 + 5 + 7 = 16 2a + 2o + 2m = 16 a + o + m =8

Total number of fruits=X Apples=X-4 Oranges=X-5 Mangoes=X-7 So (X-4)+(X-5)+(X-7)=X X=8

x=apples , y= oranges ,z=mangoes
y+z=4, x+z=5, x+y=7 solving eq we get the value of x y and z. adding x y z we get total no. of fruits.

No of Apples= x- 7 no of Oranges= x- 5 no of Mangoes= x- 4

Total= 3x- 16= x 3x- x= 2x= 16 If so x= 16/2= "8"

m+o=4
a+m=5
o+a=7
2m+2o+2a=16
m+O+a=8

Let the total number of fruits be x x-4 = Apples x-5 = oranges x-7 = Mangoes x-4+x-5+x-7 = x solve for x, x=8

X+Y+Z=N

N=X+4,N=Y+5, N=Z+7

3N= X+Y+Z+16

N=8

Let a be the number of apples in the basket, b the number of oranges, and c the number of mangoes. x is the total number of the fruits in the basket. All fruits are apples except four: a=x-4 All fruits are oranges except five: b=x-5 All fruits are mangoes except seven: c=x-7 We have: x=a+b+c By substituting a,b and c with their function-x values, we will have the following equation: x=(x-4) + (x-5) + (x-7) x= x-4+x-5+x-7 x=3x-16 2x=16 then x=8

س+ص=7 س+ع=4 ص+ع=5 .. بجمع وطرح المعادلات ينتج 8 :)

x-apples y-oranges z-mangoes x+y=7 y+z=4 x+z=5 on solving we get , x=4,y=3,z=1 so,x+y+z=8

simple.... mangoes+oranges=4, apples+mangoes=5, apples+oranges=7 then through simultaneously solving these equations, we get mangoes=1, apples=4, and oranges=3

8

Let, apple=a,b=oranges,c=mangoes b+c=4 a+c=5 a+b=7 if we solve , we get a=4,b=3 and c=1.

orange + mango = 4 apple + mango = 5 orange + apple = 7

after solving these equations we get apple =4, orange= 3, mango =1

So, total 8

a=apples, m=mangoes, o=oranges,t=total If all apples except 4, this means; t-4=a and o+m=4 If all oranges except 5, this means; t-5=o and a+m=5 If all mangoes except 7, this means t-7=m and o+a=7 so: 3t-16=a+o+m and o+m=4 3t-16=a+4 and t-4=a 3t-16=t t=8

X-4 + X-5 +X-7 = X (very easy idea)

solving ...... 3X-16 =X..........2X = 16 .........(/2) ..........X=8

Total no.of fruits=X 1.Hence for first criteria X - 4 2.for second criteria X - 5 3. for second criteria X - 7 therefore X= (X - 4)+(X - 5)+(X - 7) X = 3X - 16 2X = 16 X = 8 therefore total no. of fruits are 8 so no. of apples=4 , no. oranges=3 ,no. of mango=1,

o+m=4 a+m=5

a+o=7

2a+2o+2m=16 2(a+o+m)=16 a+o+m=16/2 a+o+m=8

First you must analyze the problem.If All are apples except 4, so the oranges & mango are equally divided 2 orange & 2 mango but in the second phrase there will be 5 fruits except mango & apple so it means that their is 1 mango & 4 apple and in 3 phrase their will be 7 apple & orange so there is 3 orange to complete the seven. Equation: 1st phrase -4 - 0 = 4 2nd phrase = 5 - 4 = 1 3rd phrase = 7 - 4 = 3 Total 8

O+M=4,A+M=5,A+O=7 solving we get M=1,A=4,O=3 therefore total no. of fruits=A+O+M=8

let total fruits=x apples=x-4 ;oranges=x-5 ;mangoes=x-7; x-4+x-5+x-7=x; 2x=16; x=8

A=X-4 O=X-5 M=X-7 A+O+M=3X-16 but A+O+M=X(total no of fruits) so X=3X-16 => X=8 A=4 O=3 M=1 now read question and see whether it satisfy or not..... it does satisfy :)

Z=sum of all numbers of fruits Apples= Z-4 Oranges= Z-5 Mangoes= Z-7

Apples + Oranges + Mangoes = Z substitution: (Z-4) + (Z-5) + (Z-7) = Z 2 Z=16 Z=8 (Z-4)

we add all of number that it gave and we gain 2(a+o+m)=16 => a+o+m=8

Apples = A ; Oranges = O ; Manggoes = M ; Total Fruits = T

; P1 => A + 4 = T ; A = T – 4 ; P2 => O + 5 = T ; O = T – 5 ; P3 => M + 7 = T ; M = T – 7

   T    = A + O + M
   T    = (T – 4) + (T – 5) + (T – 7)
   T    = 3T – 16

; T - 3T = - 16 ; -2T = - 16 ; T = -16/-2 ; T = 8 So total number of fruits is 8