Michaella presents

Katy went to buy presents for her 3 friends. She paid 1/4 of her savings for the gift for Kristy. She bought a present for Michaella with half of the remaining money. She paid €8 for a gift for Marta. How much did all the gifts for Katy's friends cost together? And how much was the gift for Kristy, and how much was the gift for Michaella?

Correct answer:

k =  5.3333
m =  8
x =  21.3333

Step-by-step explanation:


x=k+m+8
k = x/4
m = 1/2·(x-k)

k+m-x = -8
4k-x = 0
k+2m-x = 0

Pivot: Row 1 ↔ Row 2
4k-x = 0
k+m-x = -8
k+2m-x = 0

Row 2 - 1/4 · Row 1 → Row 2
4k-x = 0
m-0.75x = -8
k+2m-x = 0

Row 3 - 1/4 · Row 1 → Row 3
4k-x = 0
m-0.75x = -8
2m-0.75x = 0

Pivot: Row 2 ↔ Row 3
4k-x = 0
2m-0.75x = 0
m-0.75x = -8

Row 3 - 1/2 · Row 2 → Row 3
4k-x = 0
2m-0.75x = 0
-0.375x = -8


x = -8/-0.375 = 21.33333333
m = 0+0.75x/2 = 0+0.75 · 21.33333333/2 = 8
k = 0+x/4 = 0+21.33333333/4 = 5.33333333

k = 16/3 ≈ 5.333333
m = 8
x = 64/3 ≈ 21.333333

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