# Question

Pls help

This problem sum uses a model called the Big Box Model to simplify things. We avoid using the branching diagram as it over-complicates matters. The children in the question takes a fraction of the cookies ‘and an additional’ number of it, hence, things are a little complicated. We use the branching diagram usually when there isn’t the ‘and an additional’ phrase.

The solution above shows a step-by-step process of how we can draw this simple Big Box Model and solve this problem sum much more effectively than other methods.

We visualise the whole Big Box to represent the total number of cookies in the box originally.

At step 1, we can see that 4/7 and an additional 9 cookies were taken away.

At step 2, we can see that 7/9 of the remainder and an additional 6 cookies were taken away.

At step 3, we can see that 75% (which is also 3/4) of the remainder and an additional 4 were taken away.

At step 4, we can see that there are 22 cookies left.

Working backwards and observing the Big Box from Step 4 back to Step 1, we sum it back up to find the original number of cookies in the Big Box as seen in the solutions provided.

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I see that your child was attempting to use the branching method so will also use that.

From picture attached, I have worked backwards and colour coded each step:

In orange ink: finding # of cookies before Cheryl took

Since Cheryl took 3/4 and an additional 4 cookies, this means that what was left was 1/4 minus 4 cookies. We know that 22 cookies were left in the end.

So if we take (22 + 4 = 26), we can find 1/4.

# of cookies before Cheryl took any: 26 × 4 = 104

In purple ink: finding # of cookies before Benny took

Since Benny took 7/9 and an additional 6, this means that what was left was 2/9 minus 6 cookies.

104 + 6 = 110 (this is 2/9)
110 ÷ 2 = 55
55 × 9 = 495 (this is (9/9)

In blue ink: finding # of cookies at first