*Given
Total amount of spaghetti sauce - 240 oz.
Small jar capacity - 8 oz
Large jar capacity - 16 oz
Points:
(0, 8) and (16, 0)
(0, 30) and (15, 0)
(0, 15) and (30, 0)
(0, 16) and (8, 0)
*Solution
The only points that would be labeled by the leader would be those points that would correspond to a total amount of 240 oz of spaghetti sauce. Thus, each point should be evaluated using the following expression:
8x + 16y (EXPRESSION 1)
8x + 16y = 240 (EQUATION 1)
The expression and the equation was set up based on the condition that the x-axis corresponds to the number of small (8 oz) jars and the y-axis corresponds to the number of (16 oz) large jars.
Since pairs of intercepts are given, both points should be evaluated using the given expression and each of the results should give an answer of 240. Thus, Equation 1 must be satisfied.
Testing out each pair one by one:
1. (0,8) and (16,0)
8(0) + 16(8) = 128
8(16) + 16(0) = 128
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
2. (0,30) and (15,0)
8(0) + 16(30) = 480
8(15) + 16(0) = 120
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
3. (0,15) and (30,0)
8(0) + 16(15) = 240
8(30) + 16(0) = 240
This satisfies the condition set by Equation 1 as each of the intercepts, when evaluated using Expression 1, gives an answer of 240.
4. (0,16) and (8,0)
8(0) + 16(16) = 256
8(8) + 16(0) = 64
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
Thus, the points that the leader will be plotting on the graph are the intercepts (0,15) and (30,0).
