# Algebra Word Problems (Numbers)

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GCSE Tutorial, Solving word based problems using equations, Algebra Tutorial Higher Mathematics 2
Examples:

1. Ben is ten years older than Fred. Next year, Bob will be twice as old as Fred, How old is Fred now?
2. In a talent show there were three contestants taking part and 312 people voting. The winner has 43 more votes than the 2nd placed person and twice the number of votes as the 3rd placed person. How many votes did the winner receive?
3. Pencils cost y pence. Pens cost 10p more than twice that of a pencil. Ben buys 3 pencils and 4 pens and gets \$2.40 change from a fiver. How much does one pen cost?
4. The sum of two numbers is 39 and their difference is 9. What are the two numbers?
5. A family of 2 adults and 2 children go to the cinema. Their tickets cost a total of \$14.00. Another family of 1 adult and 4 children go to the same cinema and their bill is \$13.60. How much is an adult ticket and how much is a child ticket?

GCSE Maths - Setting up and Solving Equations (Quadratic) - Writing Higher Algebra IGCSE
Examples:

1. The areas of two triangles on the right are equal.
a) Write down an equation in x and simplify y.
b) Solve this equation and calculate the area of one of the triangles.
2. Bill enters a 30 km race. He runs the first 20 km at a speed of x km per hour and the last 10 km at (x - 5) kph. His total time for the race was 4 hours.
a) Write down an equation in terms of x and solve it.
b) What are his speeds for the two parts of the run?
3. A piece of wire is cut into 2 parts. The first part is bent into the shape of a square. The second part is bent into the shape of a rectangle with one side 4 cm long and the other side twice the length of the square’s side. Let x represent one side of the square.
a) Write down two expressions in x for the areas of the two shapes.
b) If the sum of the two areas is 105 cm2, show that x2 + 8x - 105 = 0.
c) Calculate the length of the original wire.
4. A small rectangular lawn is twice as long as it is wide. It has a path around it which is 2 m wide. The area of the path is twice the area of the lawn.
a) If the small side of the lawn is m meters, write down the dimensions of the outside edge of the path.
b) By writing down the area of the lawn in terms of x and using the answer to part a), form an equation in x.
c) Simplify this equation so that it can be written as 4(x2 - 3x - 4) = 0 and solve it.
d) Write down the dimensions of the lawn.

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