Answer to Question #269619 in Math for And

Question

Use the polya's problem solving strategy.

1. Mr. Jonas has a total of 25 chickens and cow on his farm. How many of each does he have if all together there are 76 feet?

2. Karen is thinking of a number. If you double it and subtract 7 you obtain 11. What id karen's number?

Using polya's strategy solve the given problem

In consecutive turns of a monopoly game, stacy first paid 800 pesos for a hotel. She then lost half of her money when she landed on boardwalk. Next, she collected 200 pesos for passing GO. She then lost half her remaining money when she landed on Illinois avenue. Stacy now has 2500 pesos. How much did she have just before she purchased the hotel?

Answer 1

1.

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chicken has 2 feet and cow has 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a table.

Procedure: Make a table reflecting the data in the problem. Such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

$$\begin{matrix} Chickens & Cow & Number & Number & Total \\ & & of\ chicken & of cow & number \\ & & feet & feet & of\ feet \\ \hdashline \\ 20 & 5 & 40 & 20 & 60\\ 21 & 4 & 42 & 16 & 58\\ \end{matrix}$$

We are going in the wrong direction! The total number of feet is decreasing!

$$\begin{matrix} 19 & 6 & 38 & 24 & 62\\ \end{matrix}$$

Better! The total number of feet are increasing!

$$\begin{matrix} 15 & 10 & 30 & 40 & 70\\ 12 & 13 & 24 & 52 & 76 \end{matrix}$$

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem.

2.

Solution

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

$$9 \times 2 = 18, 18 -7 = 11$$

5. We have the right answer. 9 is Karen's number.

3.

Step 1: Understanding the problem

We need to determine the number of dollars Stacey had just prior to her $800 hotel purchase.

Step 2: Devise a plan.

We could guess and check, but we might need to make several guesses before we found the correct solution. An algebraic method might work, but setting up the necessary equation could be a challenge. Since we know the end result, lets try the methods of working backwards.

Step 3: Carry out the plan

Stacy must have had $2\times2500\ pesos=5000\ pesos$ just before she landed Illinois avenue; $5000\ pesos-200\ pesos=4800\ pesos$ before she passed GO; and $2\times4800\ pesos=9600\ pesos$ prior to landing on boardwalk.

This means she had $9600\ pesos+800\ pesos=10400\ pesos$ just before she purchased the hotel.

Step 4: Looking back:

Check:

$$10400\ pesos-800\ pesos=9600\ pesos$$

$$9600\ pesos/2=4800\ pesos$$

$$4800\ pesos+200\ pesos=5000\ pesos$$

$$5000\ pesos/2=2500\ pesos$$

We have found the solution to this problem.

She had $10400\ pesos$ just before she purchased the hotel.