the average of all 5 or Carlos tests is 84. the average of his first three tests is 80. what is the average of his last two test grades?
Answers
Answer:
The average of his last two test grades is 90.
Step-by-step explanation:
Write the given information in algebraic form. State your variables first.
Let:
'a' be the grade for the first test
'b' be the grade for the second test
'c' be the grade for the third test
'd' be the grade for the fourth test
'e' be the grade for the fifth test
(a + b + c + d + e)/5 = 84 --- eq'n 1A
(a + b + c)/3 = 80 --- eq'n 2A
(d + e)/2 = x --- eq'n 3A
Note, we are solving for 'x'.
Create equivalent equations for each, to rid of the fractions.
(a + b + c + d + e)/5 = 84 --- eq'n 1A
a + b + c + d + e = 5*84
a + b + c + d + e = 420 --- eq'n 1B
(a + b + c)/3 = 80 --- eq'n 2A
a + b + c = 3*80
a + b + c = 240 --- eq'n 2B
(d + e)/2 = x --- eq'n 3A
d + e = 2x --- eq'n 3B
Substitute eq'n 2B and eq'n 3B into eq'n 1B.
a + b + c + d + e = 420
(a + b + c) + (d + e) = 420
240 + 2x = 420
Solve for 'x'.
2x = 420 - 240
2x = 180
x = 90
*The average for the two last test grades is found in eq'n 3A.
(d + e)/2 = x
Answer 90:
Step-by-step explanation: