Algebra - word problem help?

Question

I'm having trouble figuring out the equation for this problem.

Problem: Bob is having dinner, he only has $20.00. He must pay 7% sales tax and wants to leave a 15% tip on the total bill (meal plus tax), what is the maximum price of the lunch he can order?

I'm coming up with x+.07x+.15(.07x) = 20 and the answer I'm getting does not match the answer in the back of the book ($16.25)

Can anyone offer any guidance on what I'm doing incorrectly here?

Thanks in advance.

Answer 1

Let x be the price of the meal

.07x is the sales tax

The tip is assumed to be on the sum of the meal plus the sales tax

The tip is .15(x + .07x)

Add the components giving $20

x + .07x + .15(x + .07x = 20

x + .07x + .15x + .0105x = 20

1.2305x = 20

x = 16.25 +

Answer 2

The 15% is of the whole bill including tax - your equation has it just for the tax:

20 = 1.15(1.07x)

= 1.2305x

x = 20/1.2305 = 16.25

Answer 3

Solution:

the only change you need to make in your equation is:

x+.07x+0.15(x+.07x)=20

because the tip will be 15% of total bill (meal + tip i.e. x+.07x)

so x+.07x+0.15(1.07x)=20

now you will get your answer. I hope I am clear enough

Good Luck!!