SOLUTION: There are 3 times as many pears as oranges. A group of children receive 5 oranges abd 8 pears each. All the oranges are given away, but there are 21 pears left. How many children a

Let x be number of children and y the number of oranges. 

All the oranges are given away and each child has 5 oranges.

So the number of oranges is 5 times the number of children.  So
one equation is

                          y = 5x

Since there are 3 times as many pears as oranges,

the number of pears is 3 times the number of oranges, so

the number of pears = 3y

Since there were 21 pears left, 

there were only 3y-21 pears received, because we subtract the 21
from the number of pears to get the number of pears given out.

Since each child received 8 pears,

The number of pears received = 8 times the number of children.

                      3y-21 = 8x
                          
So we have this system of equations:

                          y = 5x
                      3y-21 = 8x

We use the method of substitution.  We substitute 5x
for y in the second equation.

                   3(5x)-21 = 8x
                     15x-21 = 8x   

Add +21 to both sides 

                     15x-21 = 8x                   
                        +21     +21
                    -----------------
                     15x    = 8x+21

Add -8x to both sides of the equation:

                      15x    = 8x+21
                      -8x     -8x
                    -----------------
                       7x    =    21
                     
Divide both sides by 7

                        x    =    3

Substitute x=3 into        y = 5x      
                           y = 5(3) = 15

So there were x=3 children and y=15 oranges 


That's all you were asked for but we must find the number of
pairs so we can check the problem.

Since the number of pears = 3y, 3(15) = 45

So there were 45 pears. 

Now we check the sentences in the problem, with

There are 3 times as many pears as oranges. 

That checks because 3×15 = 45

The oranges check because 5×3 = 15 

8×3 = 24 pears given out plus the 21 left over is 24+21=45
So that checks.

So 3 children, 15 oranges, and 45 pears is correct.     

Edwin