Chapter 6.5, Problem 32PFA

To determine

To check if the given statements are true.

Answer to Problem 32PFA

A, D, E, F

Explanation of Solution

Given:

	Weight of rice (in pounds)	Weight of beans (in pounds)	Total cost (in $)
Kate	3	1	4.50
Elisa	4	2	7.00

The statements given are:

Calculation:

Let x be the cost of rice and y be the cost of beans.

Given that Kate has purchased 3 pounds rice and 1 pound beans for $4.50

  $\Rightarrow 3x+y=\mathrm{4.50.............................}(1)$

  $\Rightarrow 4x+2y=\mathrm{7.00..........................}(2)$

Multiply equation (1) with 2,

  $\Rightarrow 6x+2y=\mathrm{9.00.............................}(3)$

Subtract equation (2) from equation (3), so that y is eliminated

  $\begin{array}{l}\Rightarrow (6x+2y)-(4x+2y)=9.00-7.00\\ \Rightarrow 2x=2.00\\ \Rightarrow x=1.00\end{array}$

Substitute the value of x in equation (2).

  $\begin{array}{l}\Rightarrow 4(1.00)+2y=7.00\\ \Rightarrow 4.00+2y=7.00\\ \Rightarrow 2y=3.00\\ \Rightarrow y=1.50\end{array}$

Therefore, the cost of one pound of rice is $1.00 and the cost of one pound of beans is $1.50

Conclusion:

Therefore, the correct statements are A, D, E and F.