Page 113 - Mathematics

Example 5.48 Solution
Let x be the minimum score in the
If 5 is subtracted from twice a certain second test for Vivian to pass the
number, the result is less than 11. examination. This implies that, the
Find the number. average of the scores in the two tests Tanzania Institute of Education

should be greater or equal to 61.
Solution Thus,
Let y be the required number. 1

The corresponding inequality is 2 (54 + ) x ≥ 61
5 11.
2y −< Solve the inequality to obtain the
Adding 5 on both sides gives values of x. That is,
5 5 11 5<
2y −+ + 27 + 1 x ≥ 61
2y < 16 1 2

Divide by 2 on both sides of the 2 x ≥ 34
equation to get x ≥ 68.
2y < 16

2 2 Solving for x gives x ≥ 68.
y < 8 Therefore, the lowest possible marks

Therefore, y < 8. that Vivian should obtain in the
second test is 68.

Example 5.49
Example 5.50

A minimum average mark for a In a village water project, a

candidate to pass an examination is deep well is to be drilled. The
61 in two tests. If Vivian obtained 54 temperature at x metres below
marks in the first test, find the lowest the Earth’s surface is given by
possible marks she should obtain in T = 30 25(x+ − 3), 5 ≤≤ 75
x
the second test in order to pass the where T is the temperature in degrees
examination.
of Celsius. What is the minimum Mathematics Form One
depth for the temperature to be
greater or equal to 155°?

107

25/10/2024 09:51:39
Mathematics form 1.indd 107
Mathematics form 1.indd 107 25/10/2024 09:51:39