925 USD

Four classmates saved an annual total of 925 USD. The second save twice as the first, the third 35 USD more than the second, and the fourth 10 USD less than the first. How does USD save each of them?

Correct answer:

a =  150
b =  300
c =  335
d =  140

Step-by-step explanation:


a+b+c+d=925
b=2a
c = 35+b
d = a-10

a+b+c+d=925
b=2·a
c = 35+b
d = a-10

a+b+c+d = 925
2a-b = 0
b-c = -35
a-d = 10

Pivot: Row 1 ↔ Row 2
2a-b = 0
a+b+c+d = 925
b-c = -35
a-d = 10

Row 2 - 1/2 · Row 1 → Row 2
2a-b = 0
1.5b+c+d = 925
b-c = -35
a-d = 10

Row 4 - 1/2 · Row 1 → Row 4
2a-b = 0
1.5b+c+d = 925
b-c = -35
0.5b-d = 10

Row 3 - 1/1.5 · Row 2 → Row 3
2a-b = 0
1.5b+c+d = 925
-1.6667c-0.6667d = -651.6667
0.5b-d = 10

Row 4 - 0.5/1.5 · Row 2 → Row 4
2a-b = 0
1.5b+c+d = 925
-1.6667c-0.6667d = -651.6667
-0.3333c-1.3333d = -298.3333

Row 4 - -0.33333333/-1.66666667 · Row 3 → Row 4
2a-b = 0
1.5b+c+d = 925
-1.6667c-0.6667d = -651.6667
-1.2d = -168


d = -168/-1.2 = 140
c = -651.66666667+0.66666666666667d/-1.66666667 = -651.66666667+0.66666667 · 140/-1.66666667 = 335
b = 925-c-d/1.5 = 925-335-140/1.5 = 300
a = 0+b/2 = 0+300/2 = 150

a = 150
b = 300
c = 335
d = 140

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