MATH SOLVE

3 months ago

Q:
# Kristie has taken five tests in science class. The average of all five of Kristie's test scores is 94. The average of her last three test scores is 92. What is the average of her first two test scores?

Accepted Solution

A:

Answer: The average of the first two test scores is 97.Step-by-step explanation: Given that Kristie has taken five tests in science class. The average of all five of Kristie's test scores is 94 and the average of her last three test scores is 92.We are to find the average score of her first two tests.Let a1, a2, a3, a4 and a5 be teh scores of Kristle in first , second, third, fourth and fifth tests respectively.Then, according to the given information, we have[tex]\dfrac{a1+a2+a3+a4+a5}{5}=94\\\\\Rightarrow a1+a2+a3+a4+a5=94\times5\\\\\Rightarrow a1+a2+a3+a4+a5=470~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]and[tex]\dfrac{a3+a4+a5}{3}=92\\\\\Rightarrow a3+a4+a5=92\times3\\\\\Rightarrow a3+a4+a5=276~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]Subtracting equation (ii) from equation (i), we get[tex](a1+a2+a3+a4+a5)-(a3+a4+a5)=470-276\\\\\Rightarrow a1+a2=194\\\\\Rightarrow \dfrac{a1+a2}{2}=\dfrac{194}{2}\\\\\Rightarrow \dfrac{a1+a2}{2}=97.[/tex]Thus, the average of the first two test scores is 97.