If we multiply a number by 52 and add 23 to the product, we get −712. Find the number.

Step-by-step solution

Idea: Turn the words into a linear equation, then clear the fractions by multiplying both sides by the LCM of the denominators (12).

1. Let the number be x: 52x + 23 = −712.½ mark
2. Multiply both sides by 12: 30x + 8 = −7.½ mark
3. 30x = −7 − 8 = −15, so x = −1530 = −12.1 mark

Check: 52 × (−12) = −54 = −1512; −1512 + 812 = −712 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Multiplying only some terms by 12: every term on both sides must be multiplied.
• Writing 30x = −7 + 8 = 1. The 8 moves across as −8: 30x = −15.
• Adding 23 before multiplying by 52, i.e. writing 52(x + 23). The question multiplies first, then adds.

How this can come in the exam

Try one yourself

A number multiplied by 43, plus 12, gives 176. Find it.

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