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Amiraneli [1.4K]
2 years ago
13

Jim sells used drones for 70% of the original manufacturer's purchase price of a new drone. Jim also sells new drones for 15% mo

re than the manufacturer's purchase price of a new drone. write a function to determine the total amount a customer saves if they purchase a used drone rather than a new drone from Jim's store. let x represent the manufacturer's purchase price of the drone
Mathematics
1 answer:
adell [148]2 years ago
7 0

The function for the amount saved if they purchase a used drone rather than a new drone from Jim's store is f(x) = 0.45x

He sells used drones at 70% of the price (x).

So, the selling price of a used drone is:

\mathbf{Used = 70\% \times x}

Express percentage as decimal

\mathbf{Used = 0.7 \times x}

\mathbf{Used = 0.7x}

Also, he sells new drones at 15% more of the price (x).

So, the selling price of a new drone is:

\mathbf{New= (1 + 15\%) \times x}

Express percentage as decimal

\mathbf{New= (1 + 0.15) \times x}

\mathbf{New= 1.15 \times x}

\mathbf{New= 1.15x}

The amount saved is the difference between the prices of the drones.

So, we have:

\mathbf{Saved =New - Old}

This gives

\mathbf{Saved =1.15x- 0.7x}

Subtract

\mathbf{Saved =0.45x}

Express as a function

\mathbf{f(x) = 0.45x}

Hence, the function for the amount saved is f(x) = 0.45x

Read more about proportions at:

brainly.com/question/13114933

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Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

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Amount of Mortgage - $675,250

Tenure - 30 Years

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The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

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The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

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Answer:

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