SOLUTION: the price of elaines favorite big salad at the corner restaurant is 10 cents more than the price of jerrys hamburger. after treating a group of friends to lunch, jerry is certain t

Algebra ->  Equations -> SOLUTION: the price of elaines favorite big salad at the corner restaurant is 10 cents more than the price of jerrys hamburger. after treating a group of friends to lunch, jerry is certain t      Log On


   

Question 1208699: the price of elaines favorite big salad at the corner restaurant is 10 cents more than the price of jerrys hamburger. after treating a group of friends to lunch, jerry is certain that for 10 hamburgers and 5 salads he spent more than $37.94, but no more than $46.04. including tax at 8% and a $5.00 tip. in what price range is a hamburger
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say the price of a hamburger is x. This means the price of a salad is x%2B0.10, from the first statement. The cost of the 10 hamburgers and 5 salads is therefore 10x%2B5%28x%2B0.10%29=15x%2B0.5. However, we also have to include the tax and the tip. Doing so gives 1.08%2815x%2B0.5%29%2B5=16.2x%2B5.54.
Looking at the price range, we know that 37.94%3C16.2x%2B5.54%3C=46.04. Subtracting 5.54 from the inequality gives 32.4%3C16.2x%3C=40.5. Dividing both sides by 16.2 gives 2%3Cx%3C=2.5. Therefore, the price range of a hamburger is between $2.00 and $2.50, not including $2.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
the price of elaines favorite big salad at the corner restaurant is 10 cents more than the price of jerrys
hamburger. after treating a group of friends to lunch, jerry is certain that for 10 hamburgers and 5 salads he spent
more than $37.94, but no more than $46.04. including tax at 8% and a $5.00 tip. in what price range is a hamburger

Let price of a hamburger be H
Then price of her favourite salad = H + .1
The cost of 10 hamburgers and 5 salads is GREATER THAN $37.94, but LESS THAN or EQUAL to $46.04. However, this
range includes a $5 tip and 8% sales tax. Deducting the $5 tip gives $32.94 ($37.94 - $5) and $41.04 ($46.04 - $5). 

Now, the $32.94 still includes 8% tax, so using the following PROPORTIONS, we get the "tax-less"
LOWER-RANGE (LR) and UPPER-RANGE (UR) amounts as:              
                                                       matrix%281%2C5%2C+LR%2C+%22=%22%2C+32.94%2F1.08%2C+%22=%22%2C+%22%2430.50%22%29        matrix%281%2C5%2C+UR%2C+%22=%22%2C+41.04%2F1.08%2C+%22=%22%2C+%22%2438%22%29 

Cost of 10 hamburgers and 5 salads: 10H + 5(H + .1) = 10H + 5H + .5 = 15H + .5

It can now be said the cost of the 10 hamburgers and 5 salads, less tax and tip, was more than $30.50, but no
more than $38. This gives gives us the following INEQUALITY: %22%2430.50%22+%3C+15H+%2B+.5+%3C=+%22%2438%22
                                                        matrix%282%2C1%2C+30.5+-+.5+%3C+15H+%2B+.5+-+.5+%3C=+38+-+.5%2C+30+%3C+15H+%3C=+37.5%29 -- Subtracting .5 
                                                                30%2F15+%3C+15H%2F15+%3C=+37.5%2F15 ----- Dividing by 15
                                                                 highlight_green%28%22%242%22+%3C+H+%3C=+%22%242.50%22%29

As seen above, a hamburger costs MORE than $2, but NO MORE than $2.50.