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.

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

Locations of Gas Station, Rest Area, and Pizza Shop

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

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.