14. The Excess and Shortage Problem

A teacher has a bag of sweets. If she gives 10 sweets to each of her pupils, there will be an excess of 8 sweets. If she gives 1 sweets to each of her pupils, she will need another 16 sweets. How many pupils does the teacher give the sweets to? How many sweets does she have?

Answer explanation

excess of sweets

= 8 shortage of sweets

= 16

differenceinthenumberofsweets

=1- 10

= 1

Apply formula 1to find the number of pupils.

(excess +shortage) - difference

= number of items (8 +16)÷ 1

=24

The teacher gives the sweets to 24 pupils.

Apply formulae 3 or 4 to find the number of sweets. total

=number of items × equal share for each item +excess

= 24 × 10 +8

= 248

OR

total = number of items × equal share for each item - shortage =24×11- 16

= 248

She has 248 sweets.

The leader of a group of monkeys was giving away some bananas to its followers. If it gave 5 bananas to each monkey, it needed another 2 bananas. If it gave each

monkey 4 bananas, there were 3 bananas left. How many followers did the leader have? How many bananas did the leader have?

Answer explanation

excess of bananas = 3

shortage of bananas = 2

difference in the number of bananas = 5 - 4 = 1

Apply formula 1 to find the number of monkeys.

(excess + shortage) - difference = number of items

(3 +2) ÷1=5

The leader had 5 followers.

Apply formulae 3 or 4 to find the number of bananas.

total

= number of items × equal share for each item +excess

=5×4+3

=23

OR

total

= number of items ×equal share for each item - shortage

= 5 × 5- 2

=23

The leader had 23 bananas

At a tree-planting project, each volunteer is supposed to plant the same number of trees. If each volunteer plants 5 trees, there will be 3 trees left. If each volunteer plants 3 trees, there will be 9 trees left. How many trees are planted? How many volunteers are there?

Answer explanation

excess of trees= 3 excess oftrees = 9

difference in the number of trees = 5 - 3 = 2

Apply formula 2 to find the number of volunteers.

(excess - excess) + difference = number of items

(9-3) ÷2= 3

There are 3 volunteers.

Apply formula 3 to find the number oftrees.

total = number of items × equal share for each item + excess =3×5+3

= 18

OR

=3×3+9 = 18

18 trees are planted.

A teacher has a bag of sweets. If she gives each pupil 8 sweets, she will be left with

8 sweets. If she gives each pupil 10 sweets, she

needs 4 more sweets. How many pupils does the teacher give the sweets to? How many sweets does she have?

Answer explanation

excesso rsweets= X shortage of sweets = 4

Difference ofsweets each pupil gets = 10-8=2 (8 +4) ÷ 2 = 12 ÷ 2 = 6

The teacher gives the sweets to 6 pupils. 6×8+8=56 or 6 × 10-4=56

She has 56 sweets.

A carton of oranges is to be shared among some family members. If each family member gets 5 oranges, there will be 3 oranges left in the carton. If every family member gets 7oranges, there is a shortage of 7 oranges. How many members are there in this family? How many oranges are

there in this carton?

Answer explanation

excessoforanges=3 shortage of oranges =7

Difference of oranges each family member gets =7-5=2

(3 +7)÷ 2= 10 ÷2= 5

There are 5 members in this family.

5 × 5 + 3 = 28 or 5 × 7 - 7 = 28

There are 28 oranges in this carton.

Mr Nelson is changing the water ni his fish tank. If he uses a 5-litre pail, 4 litres of water will overflow. If he uses a 3-litre pail, he needs another 4 more pails of water.

How many litres o f water are needed to fill the fish tank?

Answer explanation

excess of water = 4 l

shortage of water = 3 l × 4 = 12 l

Difference between the capacity of the two pails =56-31= 21

(4 +12) ÷2= 8

He needs 8 such pails.

8×56-41=36l or

8×3 l+121=36l 36 l of water are needed to fill the fish tank.

Greenville Primary School is organising a field trip for the pupils. If the seating capacity of each bus is 35 pupils, 5 pupils will not be able to board the bus. If the

seating capacity of each bus is 40 pupils, there will be an extra empty bus. How

many buses are needed for the field trip? How many pupils are going on the field trip?

Answer explanation

excess of pupils = 5

shortage ofpupils = 40

Difference between the seating capacity of the two buses= 40 - 35 = 5

(5 +40) ÷ 5 = 45 ÷5 = 9

9 buses are needed for the field trip.

9×35+5=320 or 9×40-40=320

320 pupils are going on the field trip.

A comic book costs $3 and a mystery book costs $5 each. If Ken spends all his money on comic books, he has $6 left. If he wants to buy mystery books, he needs another $8. How many comic or mystery books is Ken buying? How much money does he have?

Answer explanation

excess of money = $6 shortage of money = $8

Difference between the cost ofa comic book and a mystery book =$5- $3=$2

($6 +$8) ÷ $2 = $14 ÷ $2=7

Ken is buying 7 comic or mystery books.

7 × $3 + $6 = $27

He has $27.

A teacher is taking some pupils on a riverboat excursion. If each boat can take only 3 pupils, 16 pupils will not get onto the boat. If each boat can take only 5 pupils.

2 pupils will not get onto the boat. How many boats are there? How many pupils are there?

Answer explanation

excess ofpupils = 16 excess of pupils = 2

Difference of pupils on each boat = 5- 3 = 2 ( 1 6 - 2 ) ÷ 2 = 14 ÷ 2 = 7

There are 7 boats.

7×3+16=37 or 7×5+2=37

There are 37 pupils.

Mrs Bunny was giving away some carrots to her children. If each rabbit received 3 carrots, there would be an excess of7 carrots. If each rabbit was given 4 carrots,

there would be only 2 carrots left. How many children did Mrs Bunny give the carrots to? How many carrots did she have?

Answer explanation

excess of carrots = 7 excessofcarrots= 2

Difference ofcarrots each rabbit would receive= 4 - 3 = 1

(7-2) ÷1=5

Mrs Bunny gave the carrots to 5 rabbits.

5 ×3 +7=22 or 5 ×4+2=22 She had 22 carrots.