SOLUTION: brian's average mark on three tests was 78. the mark on his first test was 86 his second test was three more than his third. what mark did he get on the second and third test

Algebra ->  Linear-equations -> SOLUTION: brian's average mark on three tests was 78. the mark on his first test was 86 his second test was three more than his third. what mark did he get on the second and third test      Log On


   

Question 846871: brian's average mark on three tests was 78. the mark on his first test was 86 his second test was three more than his third. what mark did he get on the second and third test
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
To solve, we need to know how to compute an average so we can correctly set up the equation. An average is computed by added each number in a group together and then dividing that result by the total of numbers that were added together. Let's look at what we know:

Average on 3 Tests: 78
Mark on First Test: 86
Mark on Second Test: x
Mark on Third Test: y

We are told that the mark on the second test was 3 more than the mark on the 3rd test. So, we can change the Mark on Second Test to read as: y + 3:

Average on 3 Tests: 78
Mark on First Test: 86
Mark on Second Test: y + 3
Mark on Third Test: y

Now, we can set this up as an equation, based on how we compute an average of a group of numbers:

%2886%2B%28y%2B3%29%2By%29%2F3=78

Next, add everything in the numerator of the fraction on the left side of the equation, which gives us:

%2889%2B2y%29%2F3=78

Next, we need to get the y all by itself on the left side of the equal sign. To do this, we can first multiply both sides of the equation by 3, which gives us:

89%2B2y=78%2A3----->

89%2B2y=234

Next, subtract 89 from both sides of the equation:

89-89%2B2y=234-89----->

2y=145

Then, divide both sides by 2:

y=145%2F2----->

y=72.5

We have just figured out what the 3rd test score is. To find out the second test score, which we are told is 3 more than the 3rd test score, we will add 3 to 72.5, giving us 75.5.

Therefore Brian got a 75.5 and 72.5 on his second and third tests, respectively.