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Algebra: Forming and Solving Equations
Hannah can buy 6 stickers and have 54p change or she can buy 10 and have 10p change. How much money (in pence) did Hannah have to start with?

Hannah had p to start with

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Worked Solution

Let the amount of money Hannah had to start with be P pence
and let the stickers cost x pence each.
From the first purchase of 6 stickers we have: 6 x + 54 = P
From the second purchase of 10 stickers we have: 10 x + 10 = P
6 x + 54 = 10 x + 10
<=> –4 x = –44
<=>x = 11 is the price of one sticker.
Substitute this in either of the two equations for P; let's choose the first:
6×11 + 54 = P
<=>P = 120
Hannah had 120 pence to start with.

© MEI Produced by Dr Ron Knott, 28 Jan 2004
tom . button [AT] mei . org . uk 		Test reference: AlgFormSolveEqun.html?ref=83865