I have a few pages of world problems and can someone tell me how they got the answers please
thanks in advance
2. Ten years ago Bob bought an antique clock for $400. He recently had the clock
appraised and its value was assessed at $750. Assume that the relationship between
value of the clock, x, and the length of time Bob owns the clock, y, is a linear
relationship.
a. Write an equation for this relationship of x and y. Show your work and box your
equation.
b. Interpret the slope in the context of the problem ( include units). Write you answer as
a complete sentence.
c. What was the value of the clock two years ago? Write you answer as a complete
sentence.
d. When will the clock be worth $1,000? Write you answer as a complete sentence.
e. The clock does not keep time well. It losses two minutes every day. How may hours
does it lose in a year (a 365 day year – not a leap year)?
Miller’s Antiques Encyclopedia
Tags: Complete Sentence, Linear Relationship, Math Word Problems
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A) Since this is to be a linear equation, we want our equation to fit into the standard format of y=mx+b, where m is the slope (ratio of the “rise” to the “run”, and b is the y-intercept (the value of y when x is 0).
So we know that in 10 years, the value of the clock increased $350 in value – this gives us a slope (m) of 350/10 or 35.
In this particular case, we know that at 0 years of ownership (when he bought it), the value was $400; therefore, the y-intercept is 400.
That gives us the equation: y=35x+400 (where x is the number of years and y is the value). You can plug in the known 0 and 10 for x, and you will see that you get 500 and 750, respectively.
Answer A: y = 35x + 400
B) The slope is $35.00 for each year of ownership. (All I did was take the method of determining the slope and add units for this answer.)
C) To find out the value 2 years ago, we can use our equation as follows: y = 35(10 – 2) + 400 := (35)(8) + 400 := 280 + 400 := $680
Answer C (in sentence form): Two years ago, the clock was valued at six hundred eighty dollars.
D) To find out how long until the clock is worth $1,000, we simply substitute 1000 for y, and solve for x:
1000 = 35x + 400 := 600 = 35x := 17 5/35 := 17 1/7 years.
Answer D (in sentence form): In seventeen and one-seventh years, the clock will be worth one thousand dollars. (You may want to take the 1/7 year, and convert it to days).
E) If the clock loses 2 minutes per day, it will lose 365*2 minutes in one year. 365*2 = 730.
This means it will lose 730/60 hours in one year (60 minutes in an hour). 730/60 = 12 1/6 hours (or 12 hours and 10 minutes).
Answer E: 12 1/6 hours.
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