Aoife buys x books costing y pence each for £2.80. The cost of the books are then increased by 5p each. She can now buy 2 fewer books for £2.40. Form an equation and solve it to find the initial cost of each book.

Original post by Ch3rry0n

Aoife buys x books costing y pence each for £2.80. The cost of the books are then increased by 5p each. She can now buy 2 fewer books for £2.40. Form an equation and solve it to find the initial cost of each book.

Working in pence (rather than pounds) throughout, we can write down that xy = 280. You need to write down a corresponding equation for the second case, then solve the two equations simultaneously to give you the value of y.

Original post by old_engineer

Working in pence (rather than pounds) throughout, we can write down that xy = 280. You need to write down a corresponding equation for the second case, then solve the two equations simultaneously to give you the value of y.

would the following equation be something like this?

(x-2)(y+5)=240

Original post by Ch3rry0n

would the following equation be something like this?

(x-2)(y+5)=240

(x-2)(y+5)=240

Yes that looks correct.

Original post by old_engineer

Yes that looks correct.

I got to that point but afterwards Im not entirely sure what to do

Original post by Ch3rry0n

I got to that point but afterwards Im not entirely sure what to do

You now have two equations and two unknowns (x and y). The required answer is the value of y, so probably the easiest way forward is to rearrange the first equation to x = 280/y and substitute that into the second equation. Then solve for y.

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