Three friends

Cuba, Matthew, and their friend Adam worked at a part-time job over the weekend to fund a joint trip to the Alps planned for spring break.

Cuba worked diligently and earned 11,000 CZK. Matthew, however, earned only one-third of the arithmetic mean of Adam's and Cuba's earnings. Together, all three boys earned three times as much as Adam alone.

Let Adam's earnings be denoted a. Write an equation to calculate how much Adam earned.

Also determine how much Matthew earned.

Final Answer:

a =  7000
k =  11000
m =  3000

Step-by-step explanation:

k = 11000
m = (1/3)·(a+k)/2
a+k+m = 3a

k = 11000
m = (1/3)·(a+k)/2
a+k+m = 3·a

k = 11000
a+k-6m = 0
2a-k-m = 0

Pivot: Row 1 ↔ Row 3
2a-k-m = 0
a+k-6m = 0
k = 11000

Row 2 - 1/2 · Row 1 → Row 2
2a-k-m = 0
1.5k-5.5m = 0
k = 11000

Row 3 - 1/1.5 · Row 2 → Row 3
2a-k-m = 0
1.5k-5.5m = 0
3.667m = 11000


m = 11000/3.66666667 = 3000
k = 0+5.5m/1.5 = 0+5.5 · 3000/1.5 = 11000
a = 0+k+m/2 = 0+11000+3000/2 = 7000

a = 7000
k = 11000
m = 3000

Our linear equations calculator calculates it.

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