Two shopkeepers, Juma and Wan bought some items from a wholesaler. Juma bought 18 loaves of bread, 40 packets of milk and 5 bars of soap while Wan bought 15 loaves of bread, 30 packets of milk and 6 bars of soap. The price of a loaf of bread, a packet of milk and a bar of soap were sh 45, sh 50 and sh 150 respectively.

Question

Two shopkeepers, Juma and Wan bought some items from a wholesaler. Juma bought 18 loaves of bread, 40 packets of milk and 5 bars of soap while Wan bought 15 loaves of bread, 30 packets of milk and 6 bars of soap. The price of a loaf of bread, a packet of milk and a bar of soap were sh 45, sh 50 and sh 150 respectively.

a.
(I) the number of items bought by Juma and Wan using a 2 * 3 matrix.
18 40 5
15 30 6

(ii) the price of the items bought a 3 * 1 matrix
45
50
150

(b) Use the matrices in (a) above to determine the total expenditure incurred by each person and hence the difference in their expenditure

18 40 5
15 30 6
*
45
50
150
= [3560, 3075]

Answer 1

looks good to me

Answer 2

To find the number of items bought by Juma and Wan using a 2*3 matrix, we can arrange the quantities they bought as the elements of the matrix.

For Juma:
Number of loaves of bread = 18
Number of packets of milk = 40
Number of bars of soap = 5

For Wan:
Number of loaves of bread = 15
Number of packets of milk = 30
Number of bars of soap = 6

So the 2*3 matrix representing the quantities bought by Juma and Wan would be:
----------------
| 18 40 5 |
| 15 30 6 |
----------------

To find the price of the items bought, we can arrange the prices as the elements of a 3*1 matrix.

The price of a loaf of bread = sh 45
The price of a packet of milk = sh 50
The price of a bar of soap = sh 150

So the 3*1 matrix representing the prices would be:
-------
| 45 |
| 50 |
| 150 |
-------

To determine the total expenditure incurred by each person, we can multiply the matrices obtained in (a) above.

Matrix multiplication can be performed by multiplying the corresponding elements of each row of the first matrix with the corresponding elements of each column of the second matrix and adding them up.

18*45 + 40*50 + 5*150 = 3560 (expenditure for Juma)
15*45 + 30*50 + 6*150 = 3075 (expenditure for Wan)

Hence, the total expenditure incurred by Juma is sh 3560, and the total expenditure incurred by Wan is sh 3075. To find the difference in their expenditures, you can subtract the two values: 3560 - 3075 = sh 485.