Question 317490
First question :
A total of 50 juniors ande seniors were given a mathematics test. The 35 juniors
attained an average score of 80while th 15 seniors attained an average of70.
What the average score for all 50 students who took the test?
<pre><b>
{{{A=S/N}}} where A = Average, S = Sum of scores, N = number

Multiply through by N

{{{AN=S}}}

{{{S=AN}}}
</pre></b>
>>...The 35 juniors attained an average score of 80...<<
<pre><b>
Substitute 80 for A and 35 for N

{{{S=80*35}}}

{{{S=2800}}}

So the sum of the scores of the juniors was 2800
</pre></b>
>>...the 15 seniors attained an average of 70...<<
<pre><b>
{{{S=AN}}}

Substitute 70 for A and 15 for N

{{{S=70*15}}}

{{{S=1050}}}

So the sum of the scores of the seniors was 1050

So the sum of the scores of all 50 was 2800 + 1050, or 3850
</pre></b>
>>...What the average score for all 50 students who took the test?...<<
<pre><b>
{{{A=S/N}}}

Substitute 3850 for S and 50 for N

{{{A=3850/50}}}

{{{A=77}}}

</pre></b>
SECOND question :

Adam tried to compute the average of his 7 test scores. He mistakenly divided
the correct sum of all of his test scores by 6 , which yielded 84.
What is Adam's correct average test score?
<pre><b>
{{{S=AN}}}

Substitute 84 for A, and 6 for N (which should have been 7

{{{S=84*6}}}

{{{S=504}}}

Now we do it correctly. Substitute 504 for S and 7 for N

{{{A=S/N}}}

{{{A=504/7}}}

{{{A=72}}}

Edwin</pre>