Vegan shop

The shops brought 23.2 kg of goods, fruits, vegetables, and nuts. The fruit was 4.7 kg more than vegetables, and the nuts were 1.5 kilograms less than the fruit. Determine the number of fruits, vegetables, and nuts.

Correct answer:

a =  9.8
b =  5.1
c =  8.3

Step-by-step explanation:


a+b+c=23.2
a = 4.7+b
c = a-1.5

a+b+c = 23.2
a-b = 4.7
a-c = 1.5

Row 2 - Row 1 → Row 2
a+b+c = 23.2
-2b-c = -18.5
a-c = 1.5

Row 3 - Row 1 → Row 3
a+b+c = 23.2
-2b-c = -18.5
-b-2c = -21.7

Row 3 - -1/-2 · Row 2 → Row 3
a+b+c = 23.2
-2b-c = -18.5
-1.5c = -12.45


c = -12.45/-1.5 = 8.3
b = -18.5+c/-2 = -18.5+8.3/-2 = 5.1
a = 23.2-b-c = 23.2-5.1-8.3 = 9.8

a = 49/5 = 9.8
b = 51/10 = 5.1
c = 83/10 = 8.3

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