NMOS 2010 Q18

Q18 Albert had a basket of fruits which contained 35 cherries and 50 strawberries, while Calvin had another basket of fruits which contained 45 cherries and 10 strawberries. Albert gave Calvin some cherries and strawberries so that eventually, 40% of Albert’s fruit basket contained cherries and 30% of Calvin’s fruit basket contained strawberries. What was the total number of cherries and strawberries that Albert gave to Calvin?


A --> 35 C + 50 S


C --> 45 C + 10 S


3 x (35 – X) --> 2 x (50 – Y)


105 – 3 X --> 100 – 2 Y


3 X – 2 Y --> 105 – 100 = 5



7 x (10 + Y) --> 3 x (45 + X)


70 + 7 Y --> 135 + 3 X


7 Y – 3 X --> 135 – 70 = 65


5 Y --> 5 + 65 = 70


Y --> 70/5 = 14


3 X --> 5 + 2 x 14 = 33


X --> 33/3 = 11



X + Y --> 11 + 14 = 25 cherries and strawberries.