An Easy Way To Work It Out?

[Barsel]

One of the questions on 1% which was on TV on Saturday was along the lines of,
If a bat and ball cost £1.10 and the bat cost £1 more than the ball, how much was the ball?
I just couldn't work this out and wondered if there is an easy understandable way to do it. TIA

[bobbinwales]

Well the answers just obvious to me £1.05 and £0.05 but there;ll be an algebra method

[aelmpvw]

i just worked down from £1.09 1p until i reached £1.05 5p . . .

[gingejbee]

Algebra...x+y=110, x-y=100. Subtract, 2y=10, y=5 and therefore x=105.

[THECORBYLOON]

Take the difference between the two items (£1) from the overall total (£1.10) then divide that answer (10p) by two to get the cost of the lower priced item (5p).

That works for any other prices

Pen and paper cost £10 and the pen cost £7 more than the paper, how much was the paper?

£10-£7 = £3
£3 ÷ 2 = £1.50

The paper cost £1.50 and the pen cost £8.50.

[Prudie]

Gingebee's algebraic answer is correct although it would help if you can remember how to solve simultaneous equations.

In words I would try to explain that as the bat cost £1 more than the ball if you take a £1 off the total you can assume they cost the same at a total of 10p so 5p each. Put the £1 back on the bat and you get 5p and £1.05.

[Buenchico]

This is one of those cases where a 'common sense' or a 'trial and error' is actually far simpler than a mathematical one. The ball clearly can't cost very much, so there are only a few options to try and it should be easy enough to get there quickly.

Doing it mathematically means delving into simultaneous equations, as follows:

Let the price of the bat be x and the price of the ball be y.

Then, working in pence, x + y = 110 [Equation 1] because we're told that the total price is 110p.

Also, x - y = 100 [Equation 2] because we know that the difference in the prices is 100p.

Adding Equation 1 to Equation 2 yields
2x = 210

Dividing both sides by 2 gives us
x = 105

Substituting back into Equation 1 then gives
105 + y = 110

Subtracting 105 from both sides leaves us with
y = 5

[douglas9401]

Just ask the salesperson.

[bobbinwales]

..Or you could just say in real life does it matter...your buying the two together as a package and if your happy its value for money why does it matter how the total price was worked out.

[Barsel]

Since I posted this question, I see it was asked on Barry's thread by Sharon and was answered by Ferlew in a way I understand.
Sorry I can't give BA as it has also been answered the same way on here by Corby and Prudie, but thanks to you both anyway.
I went to the kind of school (way back in the day) when we were actually asked in the maths class if we would like to learn Algebra and the majority said no!
We obviously didn't think it might come in handy one day.
Thanks to all.

[THECORBYLOON]

Please Miss, PRUDIE was peeking at my answer!

[-SharonA-]

Yes, Ferlew's answer was easy to grasp.

[Prudie]

I assume you're joking :-) Your answer wasn't even there when I started, I couldn't tap my answer out on a tablet in 4 minutes.

[Barsel]

Now now children, don't be falling out over a BA. :-) xx

[Peter Pedant]

// i just worked down from £1.09 1p until i reached £1.05 5p . . .//
this is called the british museum method

( Bm collects everything and so you try all the answers until you get one)

Ginge's method is much more ellie gantay

[Peter Pedant]

Hi chris
cant you just write where the cost of the barl is ecks
x + ( x+1 ) = 1.1
tray quig 2x -1 = 1.1 and 2x = .1
x being hence (*) 0.05

(*) I like 'hence' - very maffy

[Peter Pedant]

oh yeah jokey
you know the problem: two trains 30 miles apart start go towards each other. One at ten mpoh and the other at 20 mph Fly flies to and fro between them at 75 mi an hour - how far does it fly? ( er before the trains crash )

and they asked a prof of engineering who hesitated and said 75 m

and the student said o god well done - most people try to sum the decreasing series as the fly goes in between the approaching trains

and the prof said - - I did

( trains crash after an hour and the fly therefore flies for an hour at 75 mph)