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Algebra Basics Worksheet

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Algebra Basics Worksheet

Help plan a weekend market stall. Read each question carefully, show your working where you can, and use a letter for an unknown number.

Decode the algebra

A variable is a letter that stands for a number. An expression has no equals sign; an equation says two expressions are equal. A coefficient multiplies a variable, and a constant is a number on its own.

1.The stall sells a mystery number of apples, represented by a. Which is an expression for 4 more apples than a?

4a
a + 4
a − 4
4 − a

2.A candle costs c dollars. Which statement is an equation for the cost of 3 candles being $24 altogether?

3 + c = 24
3c = 24
c − 3 = 24
24c = 3

3.In the expression 6p + 9, name the coefficient of p and the constant.

4.A plant pot costs p dollars. Write an expression for the cost of 5 pots and a $3 gift bag.

Tidy the till totals

Combine like terms: terms are like when they have the same variable part. Constants can be combined with other constants.

5.Simplify the total for two orders: 3a + 5a, where a is the price of one item.

6.A stall’s earnings are recorded as 7m + 4 + 2m − 1. Simplify the expression.

7.True or false: 5x and 5y are like terms. Explain your choice.

Balance the market books

Solve each equation by undoing operations in reverse order. Check your answer by substituting it back into the equation.

8.The stall sold x bunches of flowers and 6 more the next day, making 17 bunches. Solve x + 6 = 17.

9.Three identical plant pots cost $27 in total. Solve 3p = 27 to find the price p of one pot.

10.A customer’s total is 4c + 2 = 26 dollars: four candles plus a $2 bag. Find the candle price c.

11.A box has b apples. After 5 apples are taken out, 12 remain. Write an equation and solve to find b.

12.Challenge: A market stall charges a $4 entry fee plus $2 for each game. Write a formula for the total cost C of g games, then find the cost of 5 games.