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The ratio of the number of apples Nicole and Hannah had was 1:3. When Nicole bought 4 more apple and Hannah bought 3 more apples, the ratios became 1:2. Find the number of applles Hannah had in the end.

 May 28, 2021
 #1
avatar+33612 
+2

origianlly nicole had 1 /(1+3) = 1/4 th   and hannah had  3/4 ths

 

then n added 4    and   h added 3       to cause   n to have  1/3   and h to have  2/3

 

1/4 x = n

1/4 x + 4  = 1/3 ( x + 4 + 3)

x = original amount of apples = 20        then hannah (at the end)  had   3/4 th 0f 20 PLUS 3 = 18 apples

 May 28, 2021
 #2
avatar+1425 
+3

x + 4 : 3x + 3 = 1 : 2

x = 5

Hannah had 18 apples

 May 28, 2021
 #3
avatar+121004 
+2

N  /  H     =   1 / 3   ⇒    N  =  (1/3)  H      (1)

 

(N + 4)   / ( H + 3)  =   1/2       (2)

 

Sub  (1)   into  (2)

 

(1/3)H  + 4             1

_________   =    ____           cross-multiply

    H  +  3               2

 

 

2  [ (1/3)H  + 4  ]  =  H  +  3

 

(2/3)H   +  8   =  H  +  3

 

8 - 3   =  H  - (2/3) H

 

5   =  ( 1/3)H

 

3 *  5    =    H   =  15  =  what  Hannah  started  with

 

H  +  3   =   18   =   what Hannah  ended with

 

 

 

cool cool cool

 May 28, 2021

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