Pears and oranges

There are three times as many pears as oranges. If a group of children receives five oranges each, no oranges will be left over. If the same group of children receives eight pears each, there will be 21 pears left over. How many children and oranges are there?

Final Answer:

c =  3
o =  15

Step-by-step explanation:


p=3o
5c=o
8c+21=p

p=3·o
5·c=o
8·c+21=p

3o-p = 0
5c-o = 0
8c-p = -21

Pivot: Row 1 ↔ Row 3
8c-p = -21
5c-o = 0
3o-p = 0

Row 2 - 5/8 · Row 1 → Row 2
8c-p = -21
-o+0.625p = 13.125
3o-p = 0

Pivot: Row 2 ↔ Row 3
8c-p = -21
3o-p = 0
-o+0.625p = 13.125

Row 3 - -1/3 · Row 2 → Row 3
8c-p = -21
3o-p = 0
0.292p = 13.125


p = 13.125/0.29166667 = 45
o = 0+p/3 = 0+45/3 = 15
c = -21+p/8 = -21+45/8 = 3

c = 3
o = 15
p = 45

Our linear equations calculator calculates it.
o=15

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