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Biscuits and cereal prices problem
By Timothy Goh (P944) on Thursday, October 14, 1999 - 09:18 am:

Three packets of biscuits and two packets of cereal cost $14.70. Two packet of biscuits and four packets of cereal cost $19.00.
What is the cost of one packet of cereal?

By Richard Samworth (Rjs57) on Friday, October 15, 1999 - 03:47 pm:

Timothy,

This is a (disguised) example of a pair of simultaneous equations. Let x = the price of a packet of biscuits, and let y = the price of a packet of cereal. Then the information we are given can be represented by the equations

3x + 2y = 14.7
2x + 4y = 19

We are trying to find y. Perhaps the easiest way to do this is to multiply the first equation by 2, and the second by 3. This means that the coefficient of x in each equation is 6. Now you can subtract one equation from the other, and you should be able to solve for y.

The key idea here is to choose the numbers to multiply the equations by correctly, to give the same coefficient of x in each case. This means that the x's disappear when you subtract the equations.

I hope this is enough help for you to be able to solve the problem. If not, please write back.

Richard