two word problems.........algebra (easy for people other than me hahaha)?

Question

if you dont want to tell me what the answer is, please tell me how to do this problem. i always have trouble with these.

1) you have $32.14 to spend for a sweatshirt. the sales tax is 5%. what is the most the sweatshirt can cost?

2) you have $6.46 to spend for a dinner. there is no sales tax, but you want to leave a 15% tip. what is the most the dinner can cost?

thankyou!!!

xoxo

Answer 1

1) You have $32.14 to spend for a sweatshirt. The sales tax is 5%. What is the most the sweatshirt can cost?
= $32.14 / 1.05
= $30.61

Answer: $30.61

Proof (cost of sweatshirt + 5% based on cost is $32.14):
= cost of sweatshirt + 5% sales tax
= $30.61 + (0.05 * $30.61)
= $30.61 + $1.53
= $32.14

2) You have $6.46 to spend for a dinner. There is no sales tax, but you want to leave a 15% tip. What is the most the dinner can cost?
= $6.46 / 1.15
= $5.62

Answer: $5.62

Proof (Cost of dinner plus 15% tip based on cost of dinner):
= Cost of dinner + 15% cost of dinner
= $5.62 + (0.15 * $5.62)
= $5.62 + $0.84
= $6.46

Answer 2

This problem is easy to get wrong. Many people make the mistake of taking 5% of the final price. You must take 5% of the pre-tax price, not 5% of the price after tax has already been added! Look at it this way:

Let x = the price of sweatshirt before tax
Let y = the total price after tax

y = x + 0.05x = 1.05x

So, to find x: x = y / 1.05

x = 32.14 / 1.05 = $30.61

Use the same formula for problem #2.

x = y / 1.15

x = 6.46 / 1.15 = $5.62

Hope this helps!

Answer 3

Figure out what tax is, then divide.
So for the first one, your tax is 5% .. which in decimal form is 0.05. When you're figuring out the total with tax you want to have the original price plus the 5%. So you get 1 times the original plus an additional 0.05. = 1.05

32.14 / 1.05 = 30.609... round up to the nearest cent.
So the answer is $30.61.

To check, multiply that cost by 1.05 (original + 5%).
30.61 x 1.05 = 32.1405 .. which rounds to 32.14


Do the same for number 2) remember 15% in decimal form is 0.15

Answer 4

1) let X equal the price of the shirt.

then, X + (5%)(X) = 32.14

then, 1.05X = 32.14

then, X = 32.14/1.05 = 30.61

2) let X = the price of the dinner

then, X + (.15)(X) = 6.46

then, 1.15X = 6.46

Then, X = 6.46/1.15 = 5.62

Answer 5

1) 32.14 x 0.05 (5%) = 1.607

32.14 - 1.607 = 30.533 round the total to $30.53
do the same for question #2

15% = 0.15

Answer 6

for the first one what number plus 5% of itself = 32.14

x*1.05=32.14
x= 32.14/1.05
x=30.61

Answer 7

1) 100% - 5% = 95% the max amt the t-shirt can cost
$32.14 * 95% = $30.53

2) 100% - 15% = 85% the max amt that dinner can cost
$6.46 * 85% = $5.49

your welcome

Answer 8

1)32.14X.05=1.61
32.14-1.61=$30.53

2)6.46X.15=.97
6.46-.97=5.49