Taylor and Jillian purchased pieces of gold jewelry. Taylor purchased 0.4 oz of 18-karat gold, and Jillian purchased 1.05 oz of
14-karat gold. The table shows the amounts that they each paid for their items. Taylor Jillian Type of gold 18 karat 14 karat amount purchased (oz) 0.4 1.05 price paid ($) 375.40 768.60 How much more did Taylor pay per ounce than Jillian did? (b) Draw a graph that relates the amount of money, y, that Taylor would spend if she bought x oz of 18-karat gold. (c) On the same coordinate axes, draw a graph that relates the amount of money, y, that Jillian would spend if she bought x oz of 14-karat gold. (d) Interpret the slopes of both lines. (e) Can you see which type of gold is more expensive by looking at the graphs? Explain
2. Ryan paid $15.56 for 4 lb of peanuts. What is the cost per pound? (b) About how many pounds can Ryan buy for a dollar? Round to the nearest hundredth. (c) Draw a graph that represents the relationship between the cost and the number of pounds of peanuts Ryan bought. Label the y-axis “Cost ($)” and label the x-axis “Amount purchased (lb).” (d) What is the meaning of the slope of the line that you drew in Part (c)? (e) Draw another graph showing the same relationship. This time, label the y-axis “Amount purchased (lb)” and label the x-axis “Cost ($).” (f) What is the meaning of the slope of the line that you drew in Part (e)?
1a.) Taylors price per ounce = 375.40 / 0.4 = $938.50 Julian's price per ounce = 768.60 / 1.05 = $732 Thus Taylor paid $938.50 - $732 = $206.50 more per ounce than did Julian pay.
b.) The required graph will be a straigh line passing through the origin and the point (1, 938.5)
c.) The required graph will be a straight line passing through the origin and the point (1, 732)
d.) The slope of the line in (b) is 938.5 and the slope of the line in (c) is 732 representing the amount paid by Taylor and Julian respective per ounce.
e.) By looking at the graph, the 18 carat gold (Taylor's) is more expensive because the line is steeper than that of the other graph.
2a.) Cost per pound = $15.56 / 4lb = $3.89 per lb b) For $1, Ryan can get 4/15.56 = 0.26 lb c.) The required graph will be a straight line passing through the origin and the point (1, 3.89) d) The slope of the line is 3.89 representing the price per pound Ryan paid for peanut. e.) The required graph will be a straight line passing through the origin and the point (3.89, 1) f.) The slope of the line is 0.26 representing the number of pounds of peanut Ryan can get for $1.
The closer the points are/more uniform they are to the residual line, the better the fit. The more skewed and scattered they are, the model is a worse fit.
