Introduction to Variable Equations

Hello, everyone! Today, we are going to learn how to write variable equations to represent word problems. This means we will use letters, called variables, to stand in for numbers we don’t know yet.

What is a Variable?

A variable is a letter that represents a number. For example, if we say x, it could be any number. We use variables to help us solve problems.

Why Use Variable Equations?

Using variable equations makes it easier to understand and solve word problems. Instead of writing everything out in words, we can write it in a shorter form using numbers and letters.

Steps to Write Variable Equations

  1. Read the Problem Carefully: Understand what the problem is asking.
  2. Identify the Unknown: Find out what you need to find out. This will be your variable.
  3. Translate Words into Math: Use numbers and symbols to write an equation based on the information given.
  4. Solve the Equation: Find the value of your variable.

Example 1

Word Problem: Lucy has 5 apples. She buys x more apples. How many apples does she have now?

Step 1: Identify the unknown. Here, x represents the number of apples Lucy buys.

Step 2: Write the equation:

[ 5 + x = \text{Total Apples} ]

Example 2

Word Problem: A book costs £3. If you buy x books, how much will it cost?

Step 1: Identify the unknown. Here, x represents the number of books.

Step 2: Write the equation:

[ 3x = \text{Total Cost} ]

Key Rules to Remember

  • Always define your variable first.
  • Write down what you know and what you need to find out.
  • Keep the equation clear and simple.

Tips and Tricks

  • Use a piece of paper to jot down important numbers and words.
  • Draw a picture if it helps you understand the problem better.
  • Check your equation by thinking about whether it makes sense.

Practice Questions

Easy Level Questions

  1. Tom has 10 marbles. He gives away x marbles. How many does he have now?
  2. There are 4 birds on a tree. If y more birds come, how many birds are there now?
  3. Sarah has 8 stickers. She buys x more stickers. How many stickers does she have now?
  4. A cake has 15 slices. If z slices are eaten, how many are left?
  5. There are 3 cats in a garden. If w more cats come, how many cats are there now?
  6. Jenny has x balloons. If she has 5 more, how many does she have altogether?
  7. A box has 12 chocolates. If you eat y chocolates, how many are left?
  8. A toy costs £2. If you buy x toys, how much do you spend?
  9. A pizza has 8 slices. If z slices are eaten, how many slices remain?
  10. There are 6 apples in a basket. If you add x more apples, how many apples are in the basket?

Medium Level Questions

  1. Jamie has x pounds. He buys a toy for £5. How much money does he have left?
  2. A pack of pencils costs £2. If you buy y packs, how much do you spend?
  3. There are 15 people in a class. If x people join, how many are there in total?
  4. A jar has 10 cookies. If z cookies are taken out, how many are left?
  5. Emma has x books. She gives away 3. How many books does she have now?
  6. A ticket costs £7. If you buy y tickets, how much do you pay?
  7. There are x flowers in a garden. If you plant 5 more, how many flowers are there?
  8. A train leaves at 3 PM. If it arrives in y hours, what time will it arrive?
  9. A book has 50 pages. If you read x pages, how many pages do you have left?
  10. There are 20 students in a class. If x students leave, how many are left?

Hard Level Questions

  1. A bike costs £80. If you save x pounds each week, how many weeks will it take to buy the bike?
  2. A recipe requires x grams of sugar. If you have 200 grams, how much more do you need?
  3. A garden has x plants. If you buy 10 more plants, how many will you have?
  4. A car travels at x miles per hour. How far will it travel in 3 hours?
  5. A concert ticket costs £15. If you have x pounds, how many tickets can you buy?
  6. A family has x members. If they adopt 2 more members, how many do they have now?
  7. A jar can hold x marbles. If it currently has 10, how many more can it hold?
  8. A football match lasts x minutes. If it started at 2 PM, what time does it end?
  9. A candy bar costs £1. If you have x pounds, how many can you buy?
  10. A school has x classrooms. If they build 5 more, how many classrooms will there be?

Answers

Easy Level Answers

  1. ( 10 – x )
  2. ( 4 + y )
  3. ( 8 + x )
  4. ( 15 – z )
  5. ( 3 + w )
  6. ( x + 5 )
  7. ( 12 – y )
  8. ( 2x )
  9. ( 8 – z )
  10. ( 6 + x )

Medium Level Answers

  1. ( x – 5 )
  2. ( 2y )
  3. ( 15 + x )
  4. ( 10 – z )
  5. ( x – 3 )
  6. ( 7y )
  7. ( x + 5 )
  8. ( 3 + y )
  9. ( 50 – x )
  10. ( 20 – x )

Hard Level Answers

  1. ( \frac{80}{x} )
  2. ( x – 200 )
  3. ( x + 10 )
  4. ( 3x )
  5. ( \frac{x}{15} )
  6. ( x + 2 )
  7. ( x – 10 )
  8. ( 2 + x )
  9. ( \frac{x}{1} )
  10. ( x + 5 )

I hope you find this information helpful for understanding how to write variable equations! Remember, practice makes perfect. Keep trying, and you’ll get even better at solving word problems using variables!