GCSE(F),

There are some passengers on a bus. The number of passengers is not known: instead of guessing, call the number of passengers on the bus *n*.

There are therefore *n* passengers on the bus. At the next stop, 5 more passengers get on the bus. There are now *n* + 5 passengers on the bus.

This is an algebraic **expression**, which consists of numbers and letters describing a situation. The letter *n* is known as a **variable**, which is the value of a number where the number is not known.

The bus continues to the next stop. There are *n* more passengers waiting at the stop. As the same letter is being used, then the number of people waiting in the queue is the same as were originally on the bus. The waiting passengers get on.

There are now *n* + *n* + 5 passengers on the bus. There are two lots of *n*, plus the additional 5 passengers, on the bus. The expression for the number of people on the bus is 2*n* + 5.

1. There are *n* biscuits in a packet. I put two packets of biscuits in a tin. Write an expression for the number of biscuits in the tin.

Answer: 2*n*

Two packets, each with *n* biscuits.

2. There are *s* sweets in each bag of sweets. I pour three bags of these sweets into a jar, then I take 5 sweets out. Write an expression for the number of sweets now in the jar.

Answer: 3*s* - 5

Three lots of *s*, from the three packets; then subtract 5.

The letter *x* is often used as a variable, and can get muddled with the x sign. Mathematicians do not write 2 x *x* - the times sign is omitted and the number and letter are written together as 2*x*. The number is always written first (so 2*x*, not *x*2).

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