# Available 5472

Alena and Marta want to go on vacation together. Alena lacks CZK 300 to buy the selected ticket, and Marta has 4 times that amount left over. We know that Marta has 50% more CZK available than Alena. How much does a ticket cost?

x =  3300 Kc

### Step-by-step explanation:

m = a+a/2
x = a +300
x = m - 4·300

3a-2m = 0
a-x = -300
m-x = 1200

Row 2 - 1/3 · Row 1 → Row 2
3a-2m = 0
0.667m-x = -300
m-x = 1200

Pivot: Row 2 ↔ Row 3
3a-2m = 0
m-x = 1200
0.667m-x = -300

Row 3 - 0.66666666666667 · Row 2 → Row 3
3a-2m = 0
m-x = 1200
-0.333x = -1100

x = -1100/-0.33333333 = 3300
m = 1200+x = 1200+3300 = 4500
a = 0+2m/3 = 0+2 · 4500/3 = 3000

a = 3000
m = 4500
x = 3300

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