# Problem Solving Strategies Worksheet

Problem Solving Strategies Worksheet
• Page 1
1.
Choose the mathematical model for the following problem: A number consists of two digits whose sum is 13. If 27 is added to the number its digits are interchanged. Find the number.
 a. Applying a formula b. A matrix c. A linear equation d. A rational expression

#### Solution:

The problem can be solved by translating the statement into linear equations.

2.
Jeff and Victor can do a piece of work in 14 days. Jeff alone can do it in 22 days. In how many days can Victor alone do the same work? Choose the mathematical model for the problem.
 a. A rational equation. b. Using geometric or coordinate techniques can help in solving the problem. c. By applying a formula. d. An absolute value equation.

#### Solution:

As the problem involves rates, the mathematical model for the problem will be a rational equation.

3.
A father is 28 years older than his son. In 5 years, his age will be twice the age of his son. Choose a mathematical model to find their ages.
 a. By using geometric or coordinate techniques b. By using a linear equation c. By applying a formula d. None of the above

#### Solution:

The problem can be solved by writing a linear equation.

4.
A classroom contains equal number of boys and girls. 6 girls left to play football. The number of boys in the room is 4 less than twice the remaining number of girls. What was the original number of students present? Classify the problem.
 a. A rational equation b. A matrix or determinant c. A polynomial equation of degree 2 d. None of the above

#### Solution:

The problem can be solved by writing a linear equation.

5.
Which choice is an example of a polynomial equation that can be solved by factoring?
 a. 3$x$ + 7 = - 8 b. 3$x$ + 4$y$ = 7 and $x$ - 3$y$ = 4 c. $x$2 - 64 = 0 d. None of the above

#### Solution:

3x + 7 = - 8 is a linear equation in one variable, which cannot be solved by factoring.

3x + 4y = 7 and x - 3y = 4 is a system of equations in two variables, which cannot be solved by factoring.

x2 - 64 = 0 is a polynomial equation that can be solved by factoring the left side of the equation.

6.
Choose an appropriate mathematical model for the problem. The perimeter of a rectangular field is 280 m. If the length of the field is increased by 3 m and breadth decreased by 2 m, then the area is decreased by 56 sq.m. Find the length and breadth of the field.
 a. Applying a formula b. An absolute value equation c. By using geometric or coordinate techniques d. None of the above

#### Solution:

Using the formula: Perimeter = 2(l + b) and Area = l × b will help to solve the problem.

7.
Choose the correct mathematical model for the problem. If each of the base angles of an isosceles triangle is twice the vertex angle, find the angles of the triangle.
 a. The problem can be solved by using a rational equation b. The problem can be solved by using geometric or coordinate techniques c. The problem can be solved by using a linear equation d. None of the above

#### Solution:

Let x be the vertex angle of an isosceles triangle.

Then each of the base angles be 2x.

As the sum of the 3 angles of a triangle is 180°, so by writing a linear equation, the problem can be solved.

8.
Classify the problem: A car travels in $5\frac{1}{2}$ hours the distance covered by a bus in 2 hours. In one hour, the car covers 20 km more than the bus. Find the speed of the car and the speed of the bus.
 a. A system of equations in two variables b. A linear inequality c. A polynomial equation of degree 2 d. A matrix or determinant

#### Solution:

This is a problem involving the speed of two vehicles. That is a car and a bus.

So, it can be solved by using a system of equations in two variables.

9.
31 grams of fish food is sufficient for 6 fish for a day. How much food would 11 fish require in a day?
 a. The problem can be solved by applying a formula b. The problem can be solved by using ratio and proportions c. The problem can be solved by using geometric or coordinate techniques d. None of the above

#### Solution:

31 fish : 6 days : : 11 fish : ? days

The problem can be solved by using ratio and proportions.

10.
Two ducks and three ducklings weigh 28 lbs. Three ducks and two ducklings weigh 32 lbs. All ducks weigh the same and all ducklings weigh the same. What is the weight of 4 ducks and 3 ducklings? Choose the mathematical model for the problem.
 a. The problem can be solved by using a system of equations in two variables b. The problem can be solved by applying a formula c. The problem can be solved by using a rational equation to model the conditions of the problem d. None of the above

#### Solution:

This problem involves two unknown values. That is the weight of a duck and the weight of the duckling.

So, the problem can be solved by using a system of equations in two variables.