There are 3 times as many pears as oranges. if a group of children receives 5 oranges each, there will be no oranges left over. if the same group of children receives 8 pears each, there will be 21 pears left over. how many children and oranges are there?

3 (kids) x 5 oranges each = 15 oranges 

3 times as many pears as oranges, 15 oranges x 3 = 45 pears 

so 3 (kids) x 8 pears each = 24 pears being held 

and last 45 total pears - 24 in kids hands = 21 left over 

answers: 3 children, 15 oranges, 45 total pears 

how to: 
u have a known of 21 left over pears. and u know each kid is holding 8 pears. 
what u want to do is figure out what number of total pears we have which leaves us with the 21 left over pears in the end. by knowing that our total pears is 3 times the oranges, u simply visualize and start to play with how many kids it will take to give u a workable number of total oranges which when multiplied by 3 gives u a total number of pears which is then a perfect fit for plugging in to the left over pears equation. 

The point-slope formula states:

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where

m

is the slope and

(

x

1

y

1

)

is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

(

y

−

−

1

)

=

3

5

(

x

−

−

3

)

(

y

+

1

)

=

3

5

(

x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

)

y

+

1

=

3

5

x

+

9

5

y

+

1

−

1

=

3

5

x

+

9

5

−

1

y

+

0

=

3

5

x

+

9

5

−

5

5

y

=

3

5

x

+

4

5

The point-slope formula states:

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where

m

is the slope and

(

x

1

y

1

)

is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

(

y

−

−

1

)

=

3

5

(

x

−

−

3

)

(

y

+

1

)

=

3

5

(

x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

)

y

+

1

=

3

5

x

+

9

5

y

+

1

−

1

=

3

5

x

+

9

5

−

1

y

+

0

=

3

5

x

+

9

5

−

5

5

y

=

3

5

x

+

4

5

Step-by-step explanation: