Problem 1
The value $32.55 is the correct answer.
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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.
Answer: 70.42
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Problem 3
The value $29.50 is the correct answer.
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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
Answer: 20%
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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
Answer: She earns $18 in interest
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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
Answer: Mr. Cota started with $1500
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Problem 7
S = L - RL
S = 39 - (1/4)*39
S = 39 - 9.75
S = 29.25
Answer: $29.25 is the sale price
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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
Answer: The discount rate is 30%
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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
Answer: He spent $30.24 in total