Thread: Algebra riddle

A woman buys "x" cakes at 45p each and (x+8) cakes at 55p each. \If she wishes to have change from a £20 note work out what "x" is?

I have come up with :

0.45x+0.55(x+8)=<20

Am I on the right track?

And...

A boy buys some packets of sweets for £1.20. If the sweets had been 3p a pack cheaper he would have recieved 2 more packets for his money. How many packets did he buy?

I got 78 for my answer, is this correct?

Thanks in advance

381

0.45x+0.55(x+8)=<20

very close. Since she wishes to have change, it should be 0.45x+0.55(x+8)<20

A boy buys some packets of sweets for £1.20. If the sweets had been 3p a pack cheaper he would have recieved 2 more packets for his money. How many packets did he buy?

I got 78 for my answer, is this correct?

No. Let c be the price and p be the number of packets he originally bought.
We know that pc=120 and (p+2)(c-3) = 120. So we have 2 equations with 2 unknowns and can solve simultaneously.

For the cake question: I have the formula constructed properly, but what do i do with it now

for the sweet question: And as for the simultaneous equations i have ended up with -3p+2c=6
im sure i have gone wrong somewhere along the line, could you take me through the steps for soving this one please

thanks in advance

381

still need help on this if anyone can help?

A woman buys "x" cakes at 45p each and (x+8) cakes at 55p each. \If she wishes to have change from a £20 note work out what "x" is?

I have come up with :

0.45x+0.55(x+8)=<20

0.45x+0.55x+4.4=<20

0.45x+0.55x=15.6

x=15.6

Am I on the right track?

Hello tomh381

Originally Posted by tomh381

still need help on this if anyone can help?

A woman buys "x" cakes at 45p each and (x+8) cakes at 55p each. \If she wishes to have change from a £20 note work out what "x" is?

I have come up with :

0.45x+0.55(x+8)=<20

0.45x+0.55x+4.4=<20

0.45x+0.55x=15.6

x=15.6

Am I on the right track?

Your algebra is fine, except that, as badgerigar has pointed out, you should have x < 15.6.

The question now is: what do you do with this answer? Well, x must be a whole number, mustn't it? So if the question is asking you for the greatest value of x (and you haven't actually said that it is), then you obviously want the largest whole number that is less than 15.6. That's not very hard, is it?

Grandad

Lol, Thanks for all your help and, yes, I had realised to round down to nearest whole number, whose ever heard of 15.6 cakes!?!?!? lol

so x=15 ...HAPPY DAYS...

Thanks again folks, a great resource here