David went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. David purchased twice as many cans of soup as frozen dinners and they all collectively contain 2100 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

4 cans of soup and 2 frozen dinners.

Step-by-step explanation:

Let us call the number of cans of soup David bought, and the number of frozen dinners.

We know that David bought twice as many cans of soup as frozen dinners; therefore,

We also know that each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium—and for all items David bought, collectively they contain 2100 mg of sodium; therefore, we have

Thus, we have two equations

(1).

(2).

and we solve them by substituting the value of from equation(1) into equation(2):  

David bought 2 frozen dinners.

And the number of cans of soup bought is

David bought 4 cans of soup.  

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.