Question

There are 3 times as many pears are oranges. If a group of children receive 5 oranges each,there will be no left over.If the same group of children receive 8 oranges each, there will be 21 pears left over. How many oranges are there?

Answer 1

15 orangs

Explanation:

There are 15 oranges

Solution:

Let "x" be the number of oranges

Let "y" be the number of pears

Let "c" be the number of children

There are 3 times as many pears are oranges

Number of pears = 3 times the number of oranges

y = 3x -------- eqn 1

If a group of children receive 5 oranges each, there will be no left over

So, "c" children receives 5 oranges each, there will be no left over

number of oranges = 5(number of children)

x = 5c ------- eqn 2

If the same group of children receive 8 oranges each, there will be 21 pears left over

number of pears = 8 oranges(number of children) + 21

y = 8c + 21

Substitute eqn 1

3x = 8c + 21 ---- eqn 3

Substitute eqn 2

3(5c) = 8c + 21

15c - 8c = 21

7c = 21

c = 3

Substitute c = 3 in eqn 2

x = 5(3)

x = 15

Thus there are 15 oranges

Answer 2

There are 15 oranges

Solution:

Let "x" be the number of oranges

Let "y" be the number of pears

Let "c" be the number of children

There are 3 times as many pears are oranges

Number of pears = 3 times the number of oranges

y = 3x -------- eqn 1

If a group of children receive 5 oranges each, there will be no left over

So, "c" children receives 5 oranges each, there will be no left over

number of oranges = 5(number of children)

x = 5c ------- eqn 2

If the same group of children receive 8 oranges each, there will be 21 pears left over

number of pears = 8 oranges(number of children) + 21

y = 8c + 21

Substitute eqn 1

3x = 8c + 21 ---- eqn 3

Substitute eqn 2

3(5c) = 8c + 21

15c - 8c = 21

7c = 21

c = 3

Substitute c = 3 in eqn 2

x = 5(3)

x = 15

Thus there are 15 oranges