Question posted by Nelina from The Philippines:

Grade/Level: grade 5

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?

Answer:

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.