Vineyard

While visiting a winery, the family bought a total of 32 liters of wine in bottles of 0.7 liters and 1 liter. The ratio of the number of larger bottles to smaller bottles is 9:10. The price of a smaller bottle of wine was 120 CZK and a larger bottle was 140 CZK.
a) The number of bottles of wine in the purchase is certain.
b) What was the total price the family paid for the smaller bottles of wine?

Correct answer:

n =  38
x =  2400 Kc

Step-by-step explanation:


n=a+b
32 = 0.7a+1b
10b = 9a

n=a+b
32 = 0.7·a+1·b
10·b = 9·a

a+b-n = 0
0.7a+b = 32
9a-10b = 0

Pivot: Row 1 ↔ Row 3
9a-10b = 0
0.7a+b = 32
a+b-n = 0

Row 2 - 0.7/9 · Row 1 → Row 2
9a-10b = 0
1.778b = 32
a+b-n = 0

Row 3 - 1/9 · Row 1 → Row 3
9a-10b = 0
1.778b = 32
2.111b-n = 0

Pivot: Row 2 ↔ Row 3
9a-10b = 0
2.111b-n = 0
1.778b = 32

Row 3 - 1.77777778/2.11111111 · Row 2 → Row 3
9a-10b = 0
2.111b-n = 0
0.842n = 32


n = 32/0.84210526 = 38
b = 0+n/2.11111111 = 0+38/2.11111111 = 18
a = 0+10b/9 = 0+10 · 18/9 = 20

a = 20
b = 18
n = 38

Our linear equations calculator calculates it.
x=120a=120 20=2400 Kc



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You need to know the following knowledge to solve this word math problem:

algebrabasic functionsUnits of physical quantitiesGrade of the word problem

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