last year you could get a hamburger,fries, and coloa for $2.70. since the price of hamburger increased 20%, the prices of fries has increased 10%, and cola 60%. The same meal now costs 3.46$ if the price of a cola is now 20 cents more than that of a hamburger, what was the price of each item last year?

Question

amistre64 · Answer

c = h+.20

h + c + f = 2.70 (then)

h(.2) + c(.6) + f(.1) = 3.46  (now)

anonymous · Answer

so for then its would be 20 cents 60 cents 10 cents?

amistre64 · Answer

dont know yet :)  im thinknig I should figure the percentage of the price as well....

amistre64 · Answer

if we test out that they all cost .30 then; we can see where our guess leads us...

amistre64 · Answer

.30(3) = 2.70  so that much would be good;

.3(.2) + .3(.6) + .3(.1)
.06 +.18 +.03 = .27  is not right, so we are missing something; we went lower in price instead of higher... they should be.  the percentages should be add to 1 to account for the base price and the rise in percentage...

amistre64 · Answer

h(1.2) + c(1.6) + f(1.1) = 3.46  is more accurate equation..

amistre64 · Answer

at .30 cents then we would get:

.36 +.48 +.33 = .36 + .81 = 1.17 is better; given that my .30 was off to begin with; shoulda been .90 :)

amistre64 · Answer

h(1.2) = c(1.6) - .20  : is good for this

the total price increased by .76.  76/270 = percent changed.  which is an awful decimal so we will keep it as a fraction to make it easier on us.
................................................

h(1.2) + c(1.6) + f(1.1) = 2.70(3.46/2.70)

(c(1.6) - .20)(1.2) + c(1.6) + f(1.1) = 3.46

c(1.92) - .24  + c(1.6) + f(1.1) = 3.46

c(3.52) + f(1.1)=3.70  is what I get so far...

amistre64 · Answer

h(1.2) + c(1.6) + f(1.1) = 2.70(3.46/2.70)

c(1.6) - .20 + c(1.6) + f(1.1) = 3.46  <-- corrected for my stupidity :)

c(3.2) + f(1.1) = 3.70 is what we are looking at; not that it helps me much at the moment :)

amistre64 · Answer

ack!!..... c(3.2) + f(1.1) = 3.66  ...and thats should be right lol... we really need someone smarter then me on this  ;)

anonymous · Answer

lol thanks for all your help ;)

anonymous · Answer

so just so were absolutely clear..lol... soda is $3.20 fries are 1.10 and burger is 1.20?

amistre64 · Answer

f = 2.70 - h - c; if re can get f in terms of c this would be delightful...

f(1.1) = (3.46 -h(1.2) - c(1.6))

f = [3.46 -h(1.2) - c(1.6)]/1.1

h = [c(1.6) - .20]/1.2

now we can test this theory of mine out and see where it ends up ;)  we got everything in terms of "c"

c + h + f = 2.70

c + [c(1.6) - .20]/1.2 +  [3.46 -{[c(1.6) - .20]/1.2}(1.2) - c(1.6)]/1.1 = 2.70

   the equation editor should be able to clean that up for us:

$$c + \frac{[c(1.6) - .20]}{1.2} +  \frac{[3.66 -c(3.2)]}{1.1} = 2.70$$

amistre64 · Answer

get common denominators: (1.2)(1.1)

c(1.32) +(1.1)[c(1.6) - .20] + (1.2)[3.66 -c(3.2)] = 2.70(1.32)

c(1.32) + c(1.76) - .22 + 4.392 - c(3.84) = 3.564

c(1.32 + 1.76  - 3.84) = 3.564 +.22 -4.392

amistre64 · Answer

c(-.76) = -.608

c = .80 cents....  with alot of luck ;)

amistre64 · Answer

lets get some confidence and try to work out the rest :)

c(1.6) = price of cola today

.8(1.6) = 1.28

h(1.2) = 1.28 - .20 = 1.18 is the cost of a hamburger today.

f(1.1) = 3.46 - 1.18 - 1.28

f(1.1) = cost of fries today = 1.00   corssing fingers and typing is not a good combination :)  but im almost there lol

amistre64 · Answer

f = 1/1.1 = 0.9090909090909091 = .91

h = 1.18/1.2 = 0.9833333333333333 = .98, or .99

c = 1.28/1.6 = .80  lets add them and see if we are close :)

.80 + .91 + .98 = 2.70

2.69 = 2.70  ; so Id go with h= .99

amistre64 · Answer

h = .99; c=.80; f=.91 last year