Question

Jaci averaged 84 on her first three history exams. The first score was 67. The second score was 7 less than the third score. What did she score on the second and third exams?

Answer 1

let x = score on second exam and y = score on third exam

Answer 2

so x would be 67

Answer 3

we know that "The second score was 7 less than the third score", so we can make this equation:

x = y - 7

Answer 4

67 is the first exam score

Answer 5

the second may be 67, but we haven't gotten there yet

Answer 6

so would it be like this 67x=y-7

Answer 7

so we know this so far

first exam score: 67
second exam score: x
third exam score: y


replace x with y-7 (since x = y-7) to get

first exam score: 67
second exam score: y-7
third exam score: y

Answer 8

now you add up all 3 scores, then divide by 3 to get the average of 84 like this


(Score1 + Score2 + Score3)/3 = Average

(67 + (y-7) + y)/3 = 84

(67 + y-7 + y)/3 = 84

(2y+60)/3 = 84

2y+60 = 84*3

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y = ???

Answer 9

oh ok so i use this equation right ?:)

Answer 10

yes

Answer 11

kk one sec

Answer 12

ok

Answer 13

so you don't have to divide the 3?

Answer 14

what do you mean

Answer 15

(2y+60)/3 = 84
2y+60 = 84*3 like here how instead of dividing you multiplied 3 to 84

Answer 16

oh i multiplied both sides by 3 because in the end you want to isolate y

Answer 17

so you undo that division by 3

Answer 18

oh ok :) thnks one moment

Answer 19

ok

Answer 20

is it 96 ?

Answer 21

yep, y = 96

now find x

Answer 22

okay now do you plug in the y to the very first equation you gave me?

Answer 23

yep x = y - 7

Answer 24

is it 89

Answer 25

yep

x = 89
y = 96

Answer 26

yesss! thank you so mcuh :)

Answer 27

so going back to what we defined x and y to be (remember at the top we said "let x = score on second exam and y = score on third exam", so you can see how it all comes around full circle) we know

first exam score = 67 (given)
second exam score = 89 (just found)
third exam score = 96 (just found)

Answer 28

yw