Math Problem Solving Strategies Part -2

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Here are some simple examples, where by doing guesswork one can score well.

Example 1

Q. Tickets cost 5 dollars for children and 12 dollars for adults. A total of 20 people could go to the play. There must be at least 2 teachers to supervise the children, but no more than 10. Find all possible ways & how can school minimize the cost?

Answer:

Let x be number of children tickets.

Then, 20 - x is number of adult tickets

Cost of children tickets + cost of adult tickets = total cost

Example 2

Q. A highway has a gas station every 2 miles, a rest area every 4 miles, and a pizza shop every 3 miles. Where is the closest gas station, rest area, and pizza shop all at the same time?

Answer:

Let red be gas station, let blue be rest area, and let green be pizza shop. Quick diagram can help understanding the concept quickly.

Illustration: Example 2

Gap between the red lines represents the location of a gas station. Same goes for blue and green lines.

The vertical arrow is the point where all 3 services can be found at the same time which is 12 miles.

Alternatively, find LCM of 2,3 and 4 which is 12.

A good idea to solve problems is work backwards.

Example #3

Q. I gave one-half of my oranges plus one to the first stranger I met. Then, I gave one-half of the remaining oranges plus one to the second person I met and one-half of the remaining oranges plus one to the third person. I had one apple left at the end. How many oranges are left?

Answer:

Go backwards for solution.

Third person: Received one-half plus one. Do the reverse & give yourself one and twice

(This makes sense because giving one-half of 4 plus one means giving 2 and then 1)

Second person: Received one-half plus one. Do the reverse & give yourself one and twice

First person: Received one-half plus one. Do the reverse & give yourself one and twice

There are 22 oranges in the bag.