Question

Last year you could get a​ hamburger, fries, and a cola at​ Francisco's​ Drive-In for $2.50. Since the price of a hamburger has increased 20%, the price of fries has increased 40%, and the price of a cola has increased 50%, the same meal now costs $3.42, If the price of a cola is now 6 cents more than that of a​ hamburger, what was the price of each item last​ year?

Answer 1

Lets say that the price of a hamburger was x last year, price of a fries was y last year and price of cola was z last year. So, from the given information, we can see that

x+y+z=2.5 (since thats what the total cost last year)...........(Equation A)

This year,

The price of Hamburger=1.2x (as it increased 20%)
The price of fries=1.4y (since it increased 40%)
The price of cola=1.5z (since it increased 50%).

So, total price

1.2x+1.4y+1.5z=3.42...........(Equation B)

Also given is that the price of the cola is now 6 cents more than the price of hamburger, which means

1.5z=1.2x+.06...........(Equation C)

Now, we have 3 equations and 3 variables. So we can solve them. Lets do it step by step (also, these equations can be solved directly by inputting them into an equation solver such as Wolfram, Matlab etc).

Rearranging equation C, we get

Substituting that into equations A and B and then simplifying, we get

From first equation above, we get

Putting this into the second equation above, we get

Simplifying, we get

Solving for x, we get

x=.7

Putting this value of x back into

, we get

y=1.2

Since

, putting value of x into this, we get

z=.6.

Hence,

The price of Hamburger this year =1.2x=1.2*.7=.84
The price of fries his year=1.4y=1.4*1.2=1.68
The price of cola this year=1.5z=1.5*.6=.9.

Total price=.84+1.68+.9=3.42

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