Question

1. you earned the following marks (each out of 25) on your first five tests: 10, 21, 18, 22, 13. what mark would you have to get on the next test in order to bring your test average up to 70%? show your work.

Explanation:

Step1: Understand the average formula

The average of \( n \) numbers \( x_1, x_2, \dots, x_n \) is given by \( \text{Average}=\frac{x_1 + x_2+\dots+x_n}{n} \). Here, we have 6 tests (5 done, 1 upcoming), and we want the average to be 70% of 25. First, calculate 70% of 25: \( 0.7\times25 = 17.5 \). Let the mark on the 6th test be \( x \).

Step2: Set up the average equation

The sum of the first 5 marks is \( 10 + 21+18 + 22+13 \). Let's calculate that: \( 10+21 = 31 \), \( 31+18 = 49 \), \( 49+22 = 71 \), \( 71+13 = 84 \). The average of 6 tests should be 17.5, so using the average formula: \( \frac{84 + x}{6}=17.5 \).

Step3: Solve for x

Multiply both sides of the equation by 6: \( 84 + x=17.5\times6 \). Calculate \( 17.5\times6 = 105 \). Then, subtract 84 from both sides: \( x = 105 - 84 \).

Step4: Calculate x

\( 105-84 = 21 \).

Answer:

21