Dollars

Mother split 760 dollars between Jane, Dane, and Eva: Jane got three times more than Dane and Dane and 40 dollars more than Eva. How much does each of them?

Correct answer:

j =  480
d =  160
e =  120

Step-by-step explanation:


j+d+e = 760
j = 3d
d = 40+e

j+d+e = 760
j = 3·d
d = 40+e

d+e+j = 760
3d-j = 0
d-e = 40

Pivot: Row 1 ↔ Row 2
3d-j = 0
d+e+j = 760
d-e = 40

Row 2 - 1/3 · Row 1 → Row 2
3d-j = 0
e+1.333j = 760
d-e = 40

Row 3 - 1/3 · Row 1 → Row 3
3d-j = 0
e+1.333j = 760
-e+0.333j = 40

Row 3 + Row 2 → Row 3
3d-j = 0
e+1.333j = 760
1.667j = 800


j = 800/1.66666667 = 480
e = 760-1.3333333333333j = 760-1.33333333 · 480 = 120
d = 0+j/3 = 0+480/3 = 160

d = 160
e = 120
j = 480

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