MATHEMATICS HIGH SCHOOL

A box of cereal states that there are 81 calories in a 7-cup serving. What is the unit rate for caloriesper cup? How many calories are there in 2 cups of the cereal?

The unit rate is calorie(s) per cup.

(Simplify your answer. Type an integer, proper fraction, or mixed number.)

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AC 40)

S50 AM

9/25/2020

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Answer 1

Answer:

23.142857143 calories or 23 1/7 calories

The unit rate is calories per cup

Step-by-step explanation:

7- cup serving = 81 calories

2 cups = x calories

Cross Multiply

2 cups × 81 calories = 7 cups × x

x = 2 cups × 81 calories/7 cups

x = 23.142857143 calories or 23 1/7 calories

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Answers

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Answers

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Answers

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Answers

Answer:

what is the question exactly??

can you please elaborate...

Step-by-step explanation:

Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, the principal of the loan will be $19,450, and Dahlia will make monthly payments. Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly, and assesses a service charge of $925.00. Bank Q offers a ten-year loan with an interest rate of 5.5%, compounded monthly, and assesses a service charge of $690.85. Which loan will have the greater total finance charge, and how much greater will it be? Round all dollar values to the nearest cent.a.
Loan Q’s finance charge will be $83.73 greater than Loan P’s.
b.
Loan Q’s finance charge will be $317.88 greater than Loan P’s.
c.
Loan P’s finance charge will be $20.51 greater than Loan Q’s.
d.
Loan P’s finance charge will be $234.15 greater than Loan Q’s.

Answers

To solve this, we are going to use the loan payment formula: $P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

where

$P$ is the payment

$PV$ is the present debt

$r$ is the interest rate in decimal form

$n$ is the number of payments per year

$t$ is the time in years

For Bank P

We know from our problem that the the principal of the loan will be $19,450, so $PV=19450$ . We also know that Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly , so $t=9$ and $r=(5.8)/(100) =0.058$ . Since Dahlia will make monthly payments, and a there are 12 months in a year, $n=12$ . Lets replace the values in our formula:

$P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

$P= ( (0.058)/(12)(19450))/(1-(1+ (0.058)/(12))^(-(12)(9)) )$

$P=231.59$

Now we know that the monthly payment of Dahlia is $231.59. Since we know that she is going to make 12 monthly payments for 9 years, we can calculate the future value of the loan multiplying the amount of the monthly payments ($231.59) by the number of monthly payments (12) by the number of years (9):

$FV=(231.59)(12)(9)$

$FV=25011.72$

Now we know that she is is going to pay $25,011.72 for her loan. Finally, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,011.72), and then, we are going to add the service charge ($925.00):

$FinanceCharge=(25011.72-19450)+925$

$FinanceCharge=6486.72$

The total finance charge of bank P is $6,486.72

For Bank Q

We are going to repeat the same procedure as before.

$P=19450$ , $r=(5.5)/(100) =0.055$ , $n=12$ , and $t=12$ . Lets replace the values in our formula:

$P= ( (0.055)/(12)(19450))/(1-(1+ (0.055)/(12))^(-(12)(10)) )$

$P=211.08$

Now that we have our monthly payment, we can calculate the future value of the loan multiplying the amount of the monthly payments ($211.08) by the number of monthly payments (12) by the number of years (10):

$FV=(211.08)(12)(10)$

$FV=25329.6$

Just like before, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,329.6), and then we are going to add the service charge ($690.85):

$FinanceCharge=(25329.6-19450)+690.85$

$FinanceCharge=6570.45$

The total finance charge of bank Q is $6570.45

Notice that the finance charge of ban Q is greater than the finance charge of bank P, so we are going to subtract the finance charge of bank Q from the finance charge of bank P:

$6570.45-6486.72=83.73$

We can conclude that Loan Q’s finance charge will be $83.73 greater than Loan P’s. Therefore, the correct answer is a.

Answer:

a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.

Step-by-step explanation:

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