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# Ratios

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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
+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
+3

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

x = 5

May 28, 2021
#3
+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   May 28, 2021