On a certain project the only grades awarded were
75 and 100. If 85 students completed the project
and the average of their grades was 85, how many
earned 100?
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OpenStudy (anonymous):
tips, yummy?
OpenStudy (anonymous):
lol
OpenStudy (anonymous):
hello patrick
OpenStudy (anonymous):
x=# of students who got 75
y=# of students who got 100
x+y=85
that much we know
OpenStudy (anonymous):
x+y=85
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OpenStudy (anonymous):
and
75x+100y=85
OpenStudy (anonymous):
so just solve for y :)
OpenStudy (anonymous):
k
OpenStudy (anonymous):
x+y=85
75x+100y=85
solve for y
OpenStudy (anonymous):
100y=85-75x
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OpenStudy (anonymous):
y=17/20-3/4x
OpenStudy (anonymous):
y=7
OpenStudy (anonymous):
x=78?
OpenStudy (anonymous):
so seven people go hundreds?
OpenStudy (anonymous):
nope
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OpenStudy (anonymous):
x=78
OpenStudy (anonymous):
y=7
OpenStudy (anonymous):
those values are correct, right?
OpenStudy (anonymous):
nope :\
that would make the average 77 or 78, not 85
OpenStudy (anonymous):
im kinda confused myself now
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OpenStudy (anonymous):
yummu
OpenStudy (anonymous):
lol wat?
OpenStudy (anonymous):
t carrol is coming
OpenStudy (anonymous):
@jim_thompson5910 or @Hero
OpenStudy (anonymous):
tips carrol?
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OpenStudy (anonymous):
85 = N(75) + (85-N)(100). So, 85-N got a 100.
OpenStudy (anonymous):
Just solve for N and hence, 85-N.
OpenStudy (anonymous):
N=336.6?
OpenStudy (anonymous):
wah?
jimthompson5910 (jim_thompson5910):
yummydum's first equation is correct
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jimthompson5910 (jim_thompson5910):
the second equation is missing something
jimthompson5910 (jim_thompson5910):
75x+100y represents the sum of all the scores, you need to divide that sum by 85 since there are 85 scores
OpenStudy (anonymous):
x+y=85
jimthompson5910 (jim_thompson5910):
so the second equation should be
(75x+100y)/85 = 85
OpenStudy (anonymous):
(75x+100y)/85=85
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jimthompson5910 (jim_thompson5910):
yes
OpenStudy (anonymous):
solve for y?
jimthompson5910 (jim_thompson5910):
yes, y = # of people who got 100
OpenStudy (anonymous):
y==71.5
OpenStudy (anonymous):
y=71.4
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OpenStudy (anonymous):
y=71.5
jimthompson5910 (jim_thompson5910):
no, you should get a whole number
OpenStudy (anonymous):
ahh
OpenStudy (anonymous):
75x+100y=85 squared?
jimthompson5910 (jim_thompson5910):
good
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jimthompson5910 (jim_thompson5910):
keep going
OpenStudy (anonymous):
y=72.25-3xy?
jimthompson5910 (jim_thompson5910):
no
OpenStudy (anonymous):
ehh
OpenStudy (anonymous):
10 square root of 75=85?
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jimthompson5910 (jim_thompson5910):
x+y=85
x=85-y
-----------------
75x+100y=85^2
75x+100y=7225
75(85-y)+100y=7225
solve for y
OpenStudy (anonymous):
ahh
OpenStudy (anonymous):
ehh
OpenStudy (anonymous):
I did it too fast the first time, sorry. I re-did it and got it right. If you don't get the answer from the other helpers, let me know and I can show you.
OpenStudy (anonymous):
y=34
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jimthompson5910 (jim_thompson5910):
good
OpenStudy (anonymous):
that's the answer
OpenStudy (anonymous):
ty
OpenStudy (anonymous):
yes. that's what I also got.
OpenStudy (anonymous):
these problems are from the PSAT
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OpenStudy (anonymous):
I want to solve them efficiently in order to do well in the test