Individual 5643

The farmer harvested 300 tons of grain, of which 18 tons were barley, wheat was 250% more than oats, and rye was 40% more than wheat. How many tons of individual grains did he harvest?

Correct answer:

j =  18
o =  30
p =  105
z =  147

Step-by-step explanation:


j=18
j+p+o+z = 300
p = o + 250/100 o
z = p + 40/100 p

j=18
j+p+o+z = 300
p = o + 250/100·o
z = p + 40/100·p

j = 18
j+o+p+z = 300
350o-100p = 0
140p-100z = 0

Row 2 - Row 1 → Row 2
j = 18
o+p+z = 282
350o-100p = 0
140p-100z = 0

Pivot: Row 2 ↔ Row 3
j = 18
350o-100p = 0
o+p+z = 282
140p-100z = 0

Row 3 - 1/350 · Row 2 → Row 3
j = 18
350o-100p = 0
1.2857p+z = 282
140p-100z = 0

Pivot: Row 3 ↔ Row 4
j = 18
350o-100p = 0
140p-100z = 0
1.2857p+z = 282

Row 4 - 1.28571429/140 · Row 3 → Row 4
j = 18
350o-100p = 0
140p-100z = 0
1.9184z = 282


z = 282/1.91836735 = 147
p = 0+100z/140 = 0+100 · 147/140 = 105
o = 0+100p/350 = 0+100 · 105/350 = 30
j = 18/1 = 18

j = 18
o = 30
p = 105
z = 147

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