Source: Nan Hua Primary

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# Question

# Answer

Hi

This is a question that uses this method called the *Assumption Method. *It is almost like the *guess and check *method where you will blindly guess and check for the correct answer. But this is more organised; think of it like a more organised *guess and check* method.

The *Assumption Method *is named as such because firstly, to solve the question with the method we will assume either all items are T shirts and none are Shorts, or we can assume all are Shorts and none are T shirts. Starting off with either way is perfectly fine.

So let’s say we assume that all the items bought are T shirts and none are Shorts, it would mean that there will be 208 T shirts and 0 shorts. That would cost $2912.

Next, we will subtract 1 T shirt and add on 1 pair of shorts. Now we will have 207 T shirts and 1 pair of shorts. We will remember to keep the total number of items at 208. That would cost $2918.

Next, we will again subtract 1 T shirt and add on 1 more pair of shorts. Now we will habe 206 T shirts and 2 pairs of shorts. Again the total number of items must be kept at 208. That would cost $2924.

If we were to keep on adding one and subtracting the other 1 by 1, we notice that our total cost for the items will keep increasing by $6 each time. At this point of time, do take note that our “target” value for the total cost of items is $3050.

So from our *starting point* of $2912, we need to reach $3050. And in between those 2 values is a difference of $3050-$2912= $138.

That would also tell us that we need to take 23 steps from our starting point. Because $138 divided by $6 is 23. (remember, each step of adding one and subtracting one will change the value of the total cost by $6)

Therefore, looking back at our *starting point*, to find out the number of T shirts that we have, we take 208-23, and that will be 185. We have 185 t shirts.

Looking back at our *starting point, *to find out the number of pairs of shorts that we have, we take 0+23, and that will be 23. We have 23 pairs of shorts.

To check our answer to see if it tallies,

185 x $14 = $2590

23 x $20 = $ $460

$2590 + $460 = $3050

Hope this helps. Feel free to drop me a message if you need more help.

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