Question

Problem 13 Second Ses 2015

There are some missing numbers in the following text:
- For buying pencils and 2 pens we pay ...LL. and for buying
pencils and 3 pens we pay 7800 L.L. >>
Setting up the complete givem of the text in equations give the following system:
(4x + 2y = 5600
2x + 3y = 7800
1 Copy again the complete text according to the given system.
2 Solve, showing all the steps of calculation, the preceding system and find the price of one pencil and the price of
pen​

Answer 1

1. For buying 4 pencils and 2 pens we pay 5600 L.L. and for buying 2 pencils and 3 pens we pay 7800 L.L.

2. The price of one pencil is 150 L.L. and the price of one pen is 2,500 L.L

Explanation:

The given system of equation are;

4·x + 2·y = 5,600...(1)

2·x + 3·y = 7,800...(2)

Where x represent the price of one pencil and y represents the price of one pen

Therefore, we have;

1. For buying 4 pencils and 2 pens we pay 5600 L.L. and for buying 2 pencils and 3 pens we pay 7800 L.L.

2. By making y the subject of both equations we have;

For equation (1)

y = 5,600/2 - 4·x/2 = 2,800 - 2·x

y = 2,800 - 2·x

For equation (2)

y = 7,800/3 - 2·x/3 = 2,600 - 2·x/3

y = 2,600 - 2·x/3

Equating both values of y gives;

2,800 - 2·x = 2,600 - 2·x/3

2,800 - 2,600 = 2·x - 2·x/3

200 = 4·x/3

600 = 4·x

x = 600/4 = 150

∴ The price of one pencil = 150 L.L.

y = 2,800 - 2·x = 2,800 - 2 × 150 = 2,500

∴ The price of one pen = y = 2,500 L.L.