SOLUTION: 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?

Question 107672This question is from textbook College Algebra
: 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? This question is from textbook College Algebra

Found 2 solutions by scott8148, bucky:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x=first ... (x+x+3+x+6+x+9)/4=69.5 ... 4x+18=278
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Sally took 4 tests. You can call her unknown score on the first test x.
.
Since her score improved by 3 points on each successive test, her score on the second test
was x + 3. And on the third test she scored x + 3 + 3 = x + 6. And on the fourth and final
test she scored x + 6 + 3 = x + 9.
.
You can find her average score (A) by adding her four test grades together and dividing by 4.
In equation form this is:
.

.
collecting the like terms in the numerator results in:
.

.
But the problem tells you that her average score was 69.5 ... so substitute that value for A
to get:
.

.
Get rid of the denominator on the right side by multiplying both sides of the equation by 4.
On the left side the 69.5 times 4 multiplies out to 278. And on the left side, multiplying
by 4 just eliminates the denominator. So after this multiplication by 4 the equation changes
to:
.

.
Get rid of the 18 on the right side by subtracting 18 from both sides:
.

.
Solve for x (which is her grade on the first test) by dividing both sides by 4 and you get:
.

.
The division on the right side (260 divided by 4) results in 65. This tells you that x, her
grade on the first test, was 65.
.
Check: Sally scored 65 on her first test. Therefore, she scored 68 on her second test, 71 on
her third test and 74 on her fourth test. Her average grade for these 4 tests was:
.

.
This is the same average as the problem said it should be so our answer checks.
.
Hope this helps you to understand how to do this problem.
.
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