- 10 Marks
Question
Mini has some GH¢10 notes and some GH¢20 notes. If she has 273 notes worth a total of GH¢4,370:
Required:
i) Write down the system of linear equations. (5 marks)
ii) Solve the system of linear equations. (5 marks)
Answer
Let M be the number of GH¢10 notes and N be the number of GH¢20 notes.
i) The system of linear equations is:
M + N = 273
10M + 20N = 4370
ii) To solve the system, first solve for one variable in terms of the other from the first equation:
M = 273 − N
Substitute M in the second equation:
10 (273 − N) + 20N = 4370
2730 − 10N + 20N = 4370
2730 + 10N = 4370
10N = 4370 − 2730 = 1640
N = 1640/10 = 164
Now substitute N = 164 back into the first equation:
M + 164 = 273 ⇒ M = 273 − 164 = 109
Thus, the number of GH¢10 notes is 109 and the number of GH¢20 notes is 164.
- Tags: Algebra, Linear Equations, Simultaneous Equations, Word Problem
- Level: Level 1
- Topic: Equalities and Inequalities
- Series: MAY 2016
- Uploader: Joseph