# Model Method - Questions and Answers

Question posted by Nelina from The Philippines:

Question solved by Model Method: Kelly had three times as much money as Andy. After giving Andy \$450. Kelly had twice as much money as he.
a) How much money did Andy have in the end?
b) How much money did Kelly have at first?

Step 1: For this question, we will start with the "After" model. We first draw 2 boxes to represent the amount of money Kelly had and 1 box to represent the amount of money Andy had after the transfer of \$450 from Kelly to Andy. Step 2: Since Andy received \$450 from Kelly, we will mark out a portion of Andy's box as \$450. Step 3: Since Kelly gave Andy \$450, we will add another box in dotted lines to mark out the amount of \$450 given to Andy. Step 4: Next, we can cut the model into equal parts of unknowns after marking out all the known parts which are of equal values of \$450. Step 5: Now, we are only left with 3 equal unknown parts. We can then label the unknown part of Andy's model as 1 unit. Step 6: Similarly, we are only left with 2 equal unknown parts in Kelly's model. We can then label them as 1 unit each. Step 7: Since Kelly originally had 3 times as much money as Andy and there were already 2 unknown equal parts in Kelly's model, the remaining known parts must add up to the value of 1 unit of Kelly's money. Therefore,

1 unit ---------- 3 x \$450 = \$1350

3 units ---------- 3 x \$1350 = \$4050

\$1350 + \$450 = \$1800

(a) Andy had \$1800 in the end.

(b) Kelly had \$4050 at first.

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