Summerjob

Three students participated in the summer job. Together, they earned 1780, -. Peter got a third less than John, and Paul got 100 more than Peter. How much did each one of them cost?

Correct answer:

a =  480
b =  720
c =  580

Step-by-step explanation:


a+b+c=1780
a=b-b/3
c=100+a

a+b+c = 1780
3a-2b = 0
a-c = -100

Pivot: Row 1 ↔ Row 2
3a-2b = 0
a+b+c = 1780
a-c = -100

Row 2 - 1/3 · Row 1 → Row 2
3a-2b = 0
1.667b+c = 1780
a-c = -100

Row 3 - 1/3 · Row 1 → Row 3
3a-2b = 0
1.667b+c = 1780
0.667b-c = -100

Row 3 - 0.66666667/1.66666667 · Row 2 → Row 3
3a-2b = 0
1.667b+c = 1780
-1.4c = -812


c = -812/-1.4 = 580
b = 1780-c/1.66666667 = 1780-580/1.66666667 = 720
a = 0+2b/3 = 0+2 · 720/3 = 480

a = 480
b = 720
c = 580

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Showing 1 comment:
Smarty
Too hard to find out the answer!





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