what is the formula for figuring out what is the most i can spend for lunch out of $10.00 with a 8% tax and a 15% tip

Question

 word problem 

 

Answer 1

When possible, it is good to assign a variable to the value the problem asks you to find (so you won't forget to solve for it later).

 

Let:

   x = the maximum price of a meal

 

Translate:

   "8% tax"   means   the total is now    1.08x         [x + (8/100)x]

   "15% tip"    means   the total is now   (15/100)(1.08x)

        [note: you may also write 15% as 15/100 or 0.15 as needed]

   "out of $10.00"     means    (1.15)(1.08x) ≤ $10.00

          [note: don't be afraid of the rules for inequalities]

 

    (1.15)(1.08x) ≤ $10.00        [re-write]

                 x ≤ $8.05

     The most you can spend is $8.05.

 

To check:

   meal costs $8.05

   with 8% tax:   $8.05*1.08 = $8.69

   with 15% tip:  $8.69*1.15 = $9.99

 Also:

    meal costs $8.06

    with 8% tax:   $8.06*1.08 = $8.70

    with 15% tax:  $8.70*1.15= $10.01

Answer 2

A common mistake on this problem is to think of saving percents and write that the most you can spend for lunch is

 

10x.92x.85=$7.82. Don't subtract the .08 and .15. respectively from 1, its actually wrong.

 

The correct way is to write x(1.15)(1.08)=$10.00. Then x=8.05 which is most correct. Feel free to message me for any extra details.