Word Problem - Fraction

Question :

XiuLi has $459 and YuLi has $1560. After both of them spent equal amount of money, XiuLi has 1/4 as many money as YuLi. So how much money has YuLi spent ?

Model Methods

Different at beginning = Different after spent

So 3 units $1560 - $459 = $1101

1 unit $1101 /3 = $367

YuLi spent = XiuLi spent = $459 - $367 = $92

                                                                                              ANS : $92

Word Problem - Whole Number

Question :

At first Ali has 20 marbles more than John. After John give Ali 5 marbles, then Ali has 3 times as many marble as John. How many marbles do Ali & John has at first ?

Model Method

2 units   5 + 20 + 5 = 30

1 unit15

At first Ali has 3 x 15 -5 = 40 marbles

and John has 15 + 5 = 20 marbles

                                          ANS :  Ali has 40 marbles John has 20 marbles

Word Problem - Ratio

Question   :

A farmer has equal number of chickens and ducks. After he sold 10 chickens and 36 ducks, The ratio of chickens he has to the ratio of duck he has became 3:1. How many chickens do he had at first?

Model Methods

Different remaining = Difference sold

               

                 2 units         26

                 1 unit  13

At first the farmer had 3 x 13 + 10 = 49 chickens

Alternate Methods

Make sure both the final quantities (3 parts and 1 part) are equal. Multiply the entire column by the same number

then we have the following table

As both the chickens and ducks are having the same final quantities, we can find out the below

2 units108 - 10   =   98

1 unit  49

                                                                                                             ANS :       49 chickens