SOLUTION: lauren purchased a box of burgers for 35$ at her usual grocery store. When she got back home she saw a flyer for a different store advertising a price that was 50 cents less per b
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Question 1135052: lauren purchased a box of burgers for 35$ at her usual grocery store. When she got back home she saw a flyer for a different store advertising a price that was 50 cents less per burger. if laura has shopped at the second store she could have bought 8 more burgers for the same price
what was the price of one of the burgers lauren bought? Found 5 solutions by swincher4391, greenestamps, Alan3354, ikleyn, MathTherapy:Answer by swincher4391(1107) (Show Source):
N * B = $35
(N+8)*(B-.50) = $35
N = 35/B
(35/B+8)*(B-.50) = 35
(35+8B)/B * (B-.50) = 35
(35+8B)/(B-.5) = 35B
(35+8B) = 35B(B-.5)
(35+8B) = 35B^2 - 17.5B
35B^2 -25.5B - 35 = 0
quadratic formula
Yields two answers, but only one is positive (since we're talking about money after all).
Hence the answer is $1.43 per burger.
At the first store the price for one burger was dollars, where "n" was the number of burgers in the box.
At the second store there were (n+8) burgers in their box for the same cost of 35 dollars per box,
so the cost of one single burger was dollars.
The difference in price for one single burger is 50 cents = 0.5 dollar, which gives you an equation
- = 0.5 dollars. (1)
To solve this equation, multiply both sides by 2*n*(n+8). You will get
70(n+8) - 70n = n*(n+8).
Simplify and then solve this quadratic equation
70n + 70*8 - 70n = n^2 + 8n
n^2 + 8n - 560 = 0.
Factor left side
(n+28)*(n-20) = 0.
Only positive root n = 20 is meaningful - so it is the solution.
Answer. There were 20 burgers in the box at the first store at the price = $1.75 per one burger.
CHECK. I will check if the equation (1) is satisfied.
The price for 1 burger at the first store is = cents = 175 cents.
The price for 1 burger at the second store is dollars = = 125 cents, or exactly 0.5 dollars less.
So the problem is solved correctly (!)
Solved.
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I like this approach: it is short and straightforward, and at every step of building the base equation (1) you follow
exactly to the problem's description. It prevents you of making errors - as much as possible.
You can put this solution on YOUR website!
lauren purchased a box of burgers for 35$ at her usual grocery store. When she got back home she saw a flyer for a different store advertising a price that was 50 cents less per burger. if laura has shopped at the second store she could have bought 8 more burgers for the same price
what was the price of one of the burgers lauren bought?
Let price of each burger be B
Then we get: ------- Multiplying by LCD, B(B - .5) --------- Multiplying by 2 to CLEAR DECIMAL
4B(4B - 7) + 5(4B - 7) = 0
4B - 7 = 0 OR 4B + 5 = 0
Cost of a burger, or OR
