# Algebra riddle

• Jan 26th 2009, 01:32 PM
tomh381
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?

381
• Jan 26th 2009, 02:13 PM
Quote:

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

Quote:

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.
• Jan 26th 2009, 02:33 PM
tomh381
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

381
• Jan 26th 2009, 11:52 PM
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?
• Jan 27th 2009, 01:31 AM
Riddle
Hello tomh381
Quote:

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?