# A-level Mathematics/OCR/C1/Equations/Problems

## Contents

## Manipulating Equations[edit]

### Collecting Like Terms[edit]

### Multiplication[edit]

### Fractions[edit]

## Solving Equations[edit]

### Changing the Subject of an Equation[edit]

- Solve for x.

- Solve for z.

- Solve for y.

- Solve for x.

- Solve for b.

### Solving Quadratic Equations[edit]

Find the Roots of:

## Simultaneous Equations[edit]

**Example 1**

*At a record store, 2 albums and 1 single costs £10. 1 album and 2 singles cost £8. Find the cost of an album and the cost of a single.*

Taking an album as and a single as , the two equations would be:

You can now solve the equations and find the individual costs.

**Example 2**

*Tom has a budget of £10 to spend on party food. He can buy 5 packets of crisps and 8 bottles of drink, or he can buy 10 packets of crisps and 6 bottles of drink.*

Taking a packet of crisps as and a bottle of drink as , the two equations would be:

Now you can solve the equations to find the cost of each item.

**Example 3**

*At a sweetshop, a gobstopper costs 5p more than a gummi bear. 8 gummi bears and nine gobstoppers cost £1.64.*

Taking a gobstopper as and a gummi bear as , the two equations would be: