A vendor sells hot dogs and corn dogs at three different locations. His total sales (in hundreds) for January and February from the three locations are given in the table below.
| ||||||||||||
| Place I | 10 | 8 | 8 | 7 | ||||||||
| Place II | 8 | 6 | 6 | 7 | ||||||||
| Place III | 6 | 4 | 6 | 5 | ||||||||
Represent these tables as 3×2 matrices J and F, and answer Exercise 1., Exercise 2., Exercise 3., and Exercise 4.. problems 1 - 4.
Determine total sales for the two months, that is, find J+F.
Find the difference in sales, J−F.
If hot dogs sell for $3 and corn dogs for $2, find the revenue from the sale of hot dogs and corn dogs. Hint: Let P be a 2×1 matrix. Find (J+F)P.
If March sales will be up from February by 10%, 15%, and 20% at Place I, Place II, and Place III, respectively, find the expected number of hot dogs, and corn dogs to be sold in March. Hint: Let
R be a
1×3 matrix with entries 1.10, 1.15, and 1.20. Find
.
Determine the sums and products in the next 5 problems. Given the matrices A, B, C, and D as follows:
Let
and
, find
.
Let
, find
.
Express the following systems as
, where
A,
X, and
B are matrices.
Solve the following by the Gauss-Jordan Method. Show all work.
Two apples and four bananas cost $2.00 and three apples and five bananas cost $2.70. Find the price of each.
A bowl of corn flakes, a cup of milk, and an egg provide 16 grams of protein. A cup of milk and two eggs provide 21 grams of protein, and two bowls of corn flakes with two cups of milk provide 16 grams of protein. How much protein is provided by one unit of each of these three foods.
Solve the following inconsistent or dependent systems by using the Gauss-Jordan method.
The sum of the digits of a two digit number is 9. The sum of the number and the number obtained by interchanging the digits is 99. Find the number.
Jessica has a collection of 15 coins consisting of nickels, dimes and quarters. If the total worth of the coins is $1.80, how many are there of each? Find all three solutions.
The latest reports indicate that there are altogether 20,000 American, French, and Russian troops in Bosnia. The sum of the number of Russian troops and twice the American troops equals 10,000. Furthermore, the Americans have 5,000 more troops than the French. Are these reports consistent?