Sally took four tests in science class. On each successive test, her score improved by 3 points. If her mean score was 69.5%, what did she score on the first test?
66.5%
thanks for the answer but can you please show how you got that answer
the tests improve by 3 points, therefore:
test 1 x
test 2 x+3
test 3 x+6
test 4 x+9
the mean is the sum of the test scores divided by the number of tests. also, we know the mean = 69.5%
therefore, we get the equation:
(4x+18)/4 = 69.5%
4x+18 = 278
4x = 260
x = 65
therefore the score on the first test was 65%
To find out what Sally scored on the first test, we can use the concept of mean (average). The mean score is calculated by summing up all the scores and then dividing them by the number of tests taken.
Let's assume Sally's score on the first test is "x".
We know that on each successive test, her score improved by 3 points. So her scores on the four tests would be:
First test: x
Second test: x + 3
Third test: x + 3 + 3 = x + 6
Fourth test: x + 3 + 3 + 3 = x + 9
To find the mean score, we need to calculate the sum of all the scores and divide it by the number of tests, which is 4 in this case:
(x + x + 3 + x + 6 + x + 9) / 4 = 69.5
Now, let's solve this equation to find the value of "x":
(4x + 18) / 4 = 69.5
4x + 18 = 69.5 * 4
4x + 18 = 278
4x = 278 - 18
4x = 260
x = 260 / 4
x = 65
So Sally scored 65% on her first test.