3. Martina, Ashley, and Hans each sell boxes of strawberries for $ 1.80 each, av

Question

3. Martina, Ashley, and Hans each sell boxes of strawberries for $ 1.80 each, avocados for $ 1.20 each, and tomatoes for S0.90 each. They don't sell any other food. The number sold by each seller and each type of ood is as follows. Number sold Boxes of strawberries Avocados T 390 590 510 The table can be represented as the following matrix Martina Ashley Hans 410 430 600 650 470 460 390 410 430 A590 600 650 510 470 460 (a) Find a matrix B whose entries are the prices (in dollars) of each type of food. Make sure the product A B is defined and its entries are the amounts of money (in dollars) made by each seller overall. (b) Calculate the product A B AB =$ (c) How much money (in dollars) did Hans make overali? 4. Consider the following system of linear equations. 5x-2y =-14 -3y-z =15 4x +2y +z =-31 Solve the system by completing the steps below to produce a reduced row-echelon form. 2017 McGraw-Hill Educator An R

Explanation / Answer

Strawberries are sold for 1.8$ each; Avocados are sold for 1.2$ each and tomatoes are sold for 0.9$ each;
Thus, column matrix B will become
B =
[ 1.8
1.2
  0.9 ]
Note it has to be a column matrix for AB to be possible;

Multiplying matrix A with matrix B we get :
[ 390 410 430 ] * [ 1.8 ]
[ 590 600 650 ] [ 1.2 ]
[ 510 470 460 ] [ 0.9 ]
= [ 390*1.8 + 410*1.2 + 430*0.9]
[ 590*1.8 + 600*1.2 + 650*0.9]
[ 510*1.8 + 470*1.2 + 460*0.9]

= [ 1581
2367
1896 ]

Thus, column matrix AB representing how much each of the three sellers made is given by :
[ 1581
2367
1896 ]

From, this we can see that Hans made 1896$ overall

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.