# Family party

Anna has 5 €, Anezka has 4,60 €, and for all the money, they want to buy desserts for a family party. They decide between cakes and a pinwheel: The pinwheel is € 0.40 more expensive than the cake, and the cakes can be bought for all the money by a third more than the pinwheels. How much does each dessert cost?

t =  1.2
v =  1.6

## Step-by-step explanation:

v=0.40+t
(5+4.60)v = (1+1/3)·(5+4.60)t

v=0.40+t
(5+4.60)·v = (1+1/3)·(5+4.60)·t

t-v = -0.4
38.4t-28.8v = 0

Pivot: Row 1 ↔ Row 2
38.4t-28.8v = 0
t-v = -0.4

Row 2 - 1/38.4 · Row 1 → Row 2
38.4t-28.8v = 0
-0.25v = -0.4

v = -0.4/-0.25 = 1.6
t = 0+28.8v/38.4 = 0+28.8 · 1.6/38.4 = 1.2

t = 6/5 = 1.2
v = 8/5 = 1.6

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