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The table shows a proportional relationship between the number of cartons of eggs, 
x, and the cost of the cartons of eggs, 
y, in dollars, in Grayson City.





x

y


4
6


8
12


12
18


14
21




The cost of a carton of eggs in Branson City is twice as much as in Grayson City. Travis says that since a carton of eggs costs twice as much in Branson Clty, the equation expressing the relationshlp between the number of cartons of eggs, 
x, and the cost of the cartons of eggs, 
y, in dollars, in Branson City is 
y=2x.
Which statement is correct?
a. Travis is correct because the numbers of cartons of eggs and the costs of the cartons of eggs are all multiples of 2.
Q Travis is correct because the relationship between the cost of a carton of eggs in Branson City is twice the cost of a carton of eggs in Grayson City.
(c) Travis is incorrect since the cost of a carton of eggs in Grayson City is 
$1.50 and the cost of a carton of eggs in Branson City should be half that, or 
$0.75.
(a) Travis is incorrect since the cost of a carton of eggs in Grayson City is 
$1.50 and the cost of a carton of eggs In Branson City should be twice that, or 
$3.00.

The table shows a proportional relationship between the number of cartons of eggs, x x , and the cost of the cartons of eggs, y y , in dollars, in Grayson City.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline 44 & 66 \\\newline\hline 88 & 1212 \\\newline\hline 1212 & 1818 \\\newline\hline 1414 & 2121 \\\newline\hline\newline\end{tabular}\newlineThe cost of a carton of eggs in Branson City is twice as much as in Grayson City. Travis says that since a carton of eggs costs twice as much in Branson Clty, the equation expressing the relationshlp between the number of cartons of eggs, x x , and the cost of the cartons of eggs, y y , in dollars, in Branson City is y=2x y=2 x .\newlineWhich statement is correct?\newlinea. Travis is correct because the numbers of cartons of eggs and the costs of the cartons of eggs are all multiples of 22.\newlineQ Travis is correct because the relationship between the cost of a carton of eggs in Branson City is twice the cost of a carton of eggs in Grayson City.\newline(c) Travis is incorrect since the cost of a carton of eggs in Grayson City is $1.50 \$ 1.50 and the cost of a carton of eggs in Branson City should be half that, or $0.75 \$ 0.75 .\newline(a) Travis is incorrect since the cost of a carton of eggs in Grayson City is $1.50 \$ 1.50 and the cost of a carton of eggs In Branson City should be twice that, or y y 00.

Full solution

Q. The table shows a proportional relationship between the number of cartons of eggs, x x , and the cost of the cartons of eggs, y y , in dollars, in Grayson City.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline 44 & 66 \\\newline\hline 88 & 1212 \\\newline\hline 1212 & 1818 \\\newline\hline 1414 & 2121 \\\newline\hline\newline\end{tabular}\newlineThe cost of a carton of eggs in Branson City is twice as much as in Grayson City. Travis says that since a carton of eggs costs twice as much in Branson Clty, the equation expressing the relationshlp between the number of cartons of eggs, x x , and the cost of the cartons of eggs, y y , in dollars, in Branson City is y=2x y=2 x .\newlineWhich statement is correct?\newlinea. Travis is correct because the numbers of cartons of eggs and the costs of the cartons of eggs are all multiples of 22.\newlineQ Travis is correct because the relationship between the cost of a carton of eggs in Branson City is twice the cost of a carton of eggs in Grayson City.\newline(c) Travis is incorrect since the cost of a carton of eggs in Grayson City is $1.50 \$ 1.50 and the cost of a carton of eggs in Branson City should be half that, or $0.75 \$ 0.75 .\newline(a) Travis is incorrect since the cost of a carton of eggs in Grayson City is $1.50 \$ 1.50 and the cost of a carton of eggs In Branson City should be twice that, or y y 00.
  1. Determine Cost per Carton: First, we need to determine the cost per carton in Grayson City by using the given values in the table. We can use any pair, but let's use the first pair (4 cartons for $6)(4 \text{ cartons for } \$6). To find the cost per carton, we divide the total cost by the number of cartons: $6/4=$1.50\$6 / 4 = \$1.50 per carton.
  2. Calculate Cost in Branson City: Next, since the cost in Branson City is twice that of Grayson City, we multiply the cost per carton in Grayson City by 22. So, $1.50×2=$3.00\$1.50 \times 2 = \$3.00 per carton in Branson City.
  3. Establish Relationship between Cartons and Cost: Now, we need to establish the relationship between the number of cartons, xx, and the cost in dollars, yy, in Branson City. If one carton costs $3.00\$3.00, then for xx cartons, the cost yy would be $3.00\$3.00 * xx. Therefore, the equation should be y=3xy = 3x, not y=2xy = 2x as Travis suggested.

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