Mrs. Anderson divided $420 evenly among her children. Later, when Mrs.

Question

Mrs. Anderson divided $420 evenly among her children. Later, when Mrs. Anderson was away, Daniel, the eldest, took $5 from each of his brothers and sisters. Daniel ended up with $90. If Mrs. Anderson has more than 7 children, how many children does Mrs. Anderson have?

A. 12
B. 14
C. 16
D. 18
E. 20

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icandoit4u · Answer

ans - 12
what i did was :
total amount is 420, and daniel has 90 where he took 5 from each of the kids. went straight to the options, the first one is 12. if daniel took 5 from each then that means he took 5 from 11 kids, as 1 is himself, so 5*11=55, so daniel originally had 90-55=35, since money was equally divided, we can divide 420/35 to check the total kids, if it matches then its the ans, 420/35= 12. so total 12 kids. 
otherwise u can use the algebra way
taking n as total children
equal amount = 420/n, daniel has 420/n+(n-1)*5 
420/n+(n-1)*5=90
420+5n^2=95n
5n^2-95n+420=0
n^2-19n+84=0
(n-7)(n-12)=0, n=7 or 12
since children are more than 7 so ans is 12

onlyPlanA · Answer

Let x be the number of children.

Amount of money on each children = 420/x
Amount Daniel took from the rest of the children = 5(x - 1)
Daniel's share = 420/x

Thus, amount Daniel has = 5(x - 1) + 420/x = 90
x^2 - 18x - 84 = 0
x = 12 or x = 7
Since there are more than 7 children, x can only be 12.

IMO, answer is A.

abhishekb1352 · Answer

Each child received 420/n dollars where n is the total number of children
Now Daniel stole 5 dollars from each of his siblings and ended up with 90 dollars at last. 
so , 420/n + 5(n-1) = 90
Divide by 5 on both sides, we get
84/n + n-1 = 18
this solves to --> n^2 - 19n + 84 = 0
n^2 - 12n - 7n + 84 = 0
(n-12) (n-7) = 0
n =12 or n = 7
Since its given in the question steam that n > 7
hence the number of children is n = 12.
Option A is the right answer.

odionam · Answer

let X no. of children so Daniel amount is 420/X + (x-1)5 extra 5 from other than him so total 420/X + (X-1)5 = 90 take 5 common from both side 
84/X + (X-1) = 18 no need to solve equation try option after eliminating some choices as we can understand 84 must be multiple of x or x should be integer like 7,12,14 etc therefore neglect C D E and easily put A or B finally got a

Mrs. Anderson divided $420 evenly among her children. Later, when Mrs.

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Mrs. Anderson divided $420 evenly among her children. Later, when Mrs.

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