230 algebra De mystif ieD

5. The original amount is increased by 25%. Let x represent the original
   amount.

xx

xx

x

x

x

+=

+=

+=

=

=

02516

1025 16

1025 16

12516

16

1

.

.

(.)

.

. 225
x= 12. 8

The original box of cereal contained 12.8 ounces.

6. The total bill is the cost of the meal plus the tax on the meal plus
   the tip.
   Let x represent the cost of the meal, so the amount of the tax is 0.075x.
   The tip is 15% of the meal plus tax: (x + 0.075x = 1.075x is the price of
   the meal including tax), so, the tip is 0.15(1.075x) = 0.16125x.
   The total bill is x + 0.075x + 0.16125x. We want this to equal 45:

meal taxtip total

xx x

xx

++ =

+

0 075 0 16125 45

10075

..

. ++=
++ =

=

0 16125 45

10075 0 16125 45

1 23625 45

.

(. .)

.

x

x

x

x^445

1 23625

36 40

.

x≈.

The couple can spend $36.40 on their meal.