# Algebra Word Problems

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Examples, videos, solutions, activities and worksheets to help GCSE Maths students solve algebra word problems.

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

1. Three consecutive integers add to give 105. What are they?
2. Bob is ten years older than Fred. Next year, Bob will be twice as old as Fred. How old is Fred now?
3. In a talent show, there were 3 contestants taking part and 312 people voting. The winnwr had 43 more than the second placed person and twice the number of votes as the third placed person. How many votes did the winner receive?
4. 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?
5. The sum of two numbers is 39 and their difference is 9. What as the two numbers?
6. 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 jd £13.60. How much is an adult ticket and how much is a child ticket?
7. For the annual village fete, the vicar orders 250 bottles of drinks. He orders x bottles of lemonade and the remainder of cola. Bottles of lemonade cost 35p each and bottles of cola cost 38p each. He spends £91.70 altogether. How many bottles of lemonade were purchased?
8. Given that the area of each triangle below is the same, find the dimensions of each.
9. Bill and Dan take part in a fun run. Bill’s average speed is (x + 4) kph and Dan’s is (3x) kph. Bill completes his run in (x - 1) hours and Dan in (x - 2) hours. What is Bill’s average speed?
10. 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.

Solving word problems involving percentages
Example:
Mr. Watkins oil tank holds 1500 l. It already has 850 l. Oil costs 67.2 pence per litre and he gets 5% discount. What will be the cost of filing the tank?

Ratio: Solving simple word problems involving ratio and shape and space
Example:
A triangle, square and pentagon have a total area of 48cm2. The area of the shape are in the ratio of their number of sides. Find the area of the pentagon.

Algebra: how to solve word problems
GCSE Maths revision practice paper 3
Example:
Adam has £500. Beth has £130. Adam gives some money to Beth. He now has twice as much as Beth. How much did he give away?

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