Question

problem 3
the graph shows the cost vs. weight relationship for two typ
rice that can be bought at a bulk food store.
select all of the true statements.
it costs $8 to buy 12 pounds of conventional
rice.
the cost as a unit rate for conventional rice is $1.50 per
pound.
the relationship between cost, c, and weight, w, for organ
rice can be represented by the equation c = 3w.
conventional rice costs twice as much per pound as organi
rice.
the cost vs. weight relationships for both organic and
conventional rice are proportional relationships.

Explanation:

Step1: Check the first statement

For conventional rice, when \(w = 8\), \(c=12\). The unit rate \(r=\frac{c}{w}=\frac{12}{8} = 1.5\) dollars per pound. When \(w = 12\), \(c=1.5\times12=18
eq8\). So the statement "It costs $8 to buy 12 pounds of conventional rice" is false.

Step2: Check the second statement

For conventional rice, using the formula \(r=\frac{c}{w}\). Taking a point \((w = 8,c = 12)\), \(r=\frac{12}{8}=1.5\) dollars per pound. So the statement "The cost as a unit rate for conventional rice is $1.50 per pound" is true.

Step3: Check the third statement

For organic rice, when \(w = 6\), \(c = 16\). If \(c = 3w\), then when \(w = 6\), \(c=3\times6 = 18
eq16\). The unit rate for organic rice \(r=\frac{16}{6}=\frac{8}{3}\approx2.67\). So the statement "The relationship between cost, \(c\), and weight, \(w\), for organic rice can be represented by the equation \(c = 3w\)" is false.

Step4: Check the fourth statement

Unit - rate of conventional rice \(r_{c}=1.5\) dollars per pound, unit - rate of organic rice \(r_{o}=\frac{8}{3}\approx2.67\). \(1.5
eq2\times\frac{8}{3}\). So the statement "Conventional rice costs twice as much per pound as organic rice" is false.

Step5: Check the fifth statement

Since both graphs of cost vs. weight for organic and conventional rice are straight lines passing through the origin \((0,0)\), they are proportional relationships (in the form \(y = kx\) where \(k\) is the constant of proportionality and \(y = 0\) when \(x = 0\)). So the statement "The cost vs weight relationships for both organic and conventional rice are proportional relationships" is true.

Answer:

The 2 5 statements are true