IMAT 2011 Q35 [Small Change]

I have far too much small change in my pocket: 6 x 1c coins, 3 x 2c coins, 2 x 5c coins, 3 x 10c coins and 2 x 50c coins.

I want to buy a chocolate bar for 37c using as many coins as possible.

What is the largest number of coins I can use to pay the exact price?

A. 5

B. 9

C. 10

D. 12

E. 14

Some Quick Questions to ask yourself when doing this type of problem solving:

  • What is being asked? Underline the specifics in the question.
  • Analyse the data, is there anything we can eliminate immediately?
  • What information do I need to solve the question? Where can I find it?
  • How can I draw or use the graph to help me?

We can immediately exclude all 50c coins from our solution because we need to pay exact change and the total is only 37c

Strategy, try to use up all the 1c coins, then 2c coins, etc…

Attempt: If we use all 1c coins and 2c coins, we have: 6(1c) + 3(2c) = 12c

Now, we can only add one of the 5c coins because the answer ends in 7, so we can achieve this by doing 1(5c) + 12c = 17c.

Finally we two 10c coins to get: 2(10c) + 17c = 37c.

Summary

6(1c)

3(2c)

1(5c)

2(10c)

6 + 3 + 1 + 2 = 12

Therefore D is the answer.