Susan and ronald dugan agreed upon the price of 256,000 for their new home. They plan to make 30 percent down payment and financ
1 answer:
Answer:
The total amount due for purchasing the new home comes to $838,014.72
Step-by-step explanation:
Provided are:
The price set for the new house is $256,000
The down payment intended is 30% of the house price
Therefore, the down payment totals = 30% of $256,000
i.e. The down payment equals to × 256000
Or, The down payment price computes to $76,800
Next, the remaining amount is financed
Thus, The financing amount is p = $256000 - $76800 = $179,200
The interest rate applied = r = 7.5%
The duration for financing = t = 20 years
Let The Amount after 20 years of financing be $A
Let the overall sum payable for the new home = $B
Using Compound Interest
Amount = Principal ×
Or, A = p ×
Or, A = $179,200 ×
Or, A = $179,200 ×
Or, A = $179,200 × 4.24785
∴ A = $761,214.72
Therefore,The Amount to be paid after 20 years of financing = A = $761,214.72
Subsequently
The final amount to be paid for the new home = Down payment total + The Amount to be paid after 20 years of financing
Or, B = $76,800 + A
Or, B = $76,800 + $761,214.72
Or, B = $838,014.72
Therefore, the overall amount due for the new home is rounded to $838,014.72 Answer
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Utilize the details to create inequalities that reflect each limitation or requirement.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
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</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
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</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
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4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
<span />
4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.
Answer:
The equivalent expression for the provided complex fraction is
Step-by-step explanation:
To simplify the complex fraction, calculating the numerator and denominator individually is effective.
Numerator:
Denominator:
Resolving the complex fraction:
Common terms in the numerator and denominator will cancel out (Cross multiplication):