Can anyone help! I have done 1 and 3 but I’m lost on the rest! Will give extra points!

Problem 1

Problem 2

In the previous problem, we knew the value of P to find the value of C

For this current problem, it's the reverse situation. This time we know that C = 75 and we use this to find P

In this case, R = 0.065

P + RP = C

P(1+R) = C

P(1+0.065) = 75

1.065P = 75

P = 75/(1.065)

P = 70.4225352 approximately

P = 70.42 after rounding to the nearest penny

The highest price she can afford is $70.42, which is the cost before tax. The cost after tax would be the $75 mentioned.

Problem 3

Problem 4

When it comes to tipping problems, think of it like a sales tax.

We don't know what the tip percentage rate is, so R is unknown and we need to solve for it.

The old price is P = 35 and it increases to C = 42 after the tip is included.

P + RP = C

P(1+R) = C

35(1+R) = 42

1+R = 42/35

1+R = 1.2

R = 1.2-1

R = 0.20

Problem 5

Assuming her account uses simple interest (and not compound interest), then we compute the simple interest like this

i = P*r*t

i = 400*0.045*1

i = 18

Problem 6

This is going to use the same formula as problem 5. This time we don't know what P is

i = P*r*t

105 = P*0.07*1

105 = 0.07P

0.07P = 105

P = 105/(0.07)

P = 1500

Problem 7

S = L - RL

S = 39 - (1/4)*39

S = 39 - 9.75

S = 29.25

Problem 8

S = L - RL

14 = 20 - R*20

14 = 20(1 - R)

14/20 = 1-R

0.70 = 1-R

0.70+R = 1

R = 1 - 0.70

R = 0.30

Problem 9

Each shirt costs $12 originally, but they are on sale for 20% off. Let's compute the sale price (S)

S = L - RL

S = 12 - 0.20*12

S = 12 - 2.40

S = 9.60

The sale price is $9.60 per shirt. Three of them will cost 3*9.60 = 28.80 dollars before tax.

The cost after tax is...

C = P + RP

C = 28.80 + 0.05*28.80

C = 28.80 + 1.44

C = 30.24