# Excess and Shortage Questions

The objective of this math revision note is to enhance your child’s understanding and proficiency in solving excess and shortage questions.

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## Excess and Shortage Question 1

Mrs Tan bought some sweets to distribute to her class.
If she gives each student 6 sweets, she will have 8 sweets left.
If she gives each student 8 sweets, she will be 6 sweets short.
How many sweets does Mrs Tan have?

Solutions for (a)

In the 1st scenario, every student receives 6 sweets.

In the 2nd scenario, every student receives 8 sweets.

Hence each student receives 2 more sweets in the 2nd scenario than that of the 1st scenario.

Difference in each student = 8 – 6 = 2

When we compare the total number of sweets in the 1st scenario to that of the 2nd scenario, we can see that the 2nd scenario requires 14 more sweets.

Total difference = 8 + 6 = 14

Comparing the 2nd scenario to that of the 1st scenario:

Since every student gets 2 more sweets and they receive 14 more sweets in total, we can find the number of students as such:

14 ÷ 2 = 7 students

We can find the total number of sweets by either using the 1st or 2nd scenario:

Using 1st scenario:

7 x 6 + 8 = 50 (Ans)

Using 2nd scenario:

7 × 8 – 6 = 50 (Ans)

Alternative solutions for (b)

1u = the number of students

2u = 8 + 6 = 14

1u = 14 ÷ 2 = 7 students

We can find the total number of sweets by either using the 1st or 2nd scenario:

Using 1st scenario:

7 × 6 + 8 = 50 (Ans)

Using 2nd scenario:

7 × 8 – 6 = 50 (Ans)

## Excess and Shortage Question 2

Tim packed 4 balls into each bag and found that he had 12 balls left over. If he packed 7 balls into each bag, he would need another 6 more balls. Find the number of bags he has.

Solutions

Difference in each bag = 7 – 4 = 3

Each bag has 3 more balls in the 2nd scenario compared to that of the 1st scenario.

Total difference = 12 + 6 = 18

In the 2nd scenario, the bags have 18 more balls in total compared to that of the 1st scenario.

Comparing the 2nd scenario to that of the 1st scenario:

Since every bag has 3 more balls and the bags receive 18 more balls in total, we can find the number of bags as such:

Number of bags = 18 ÷ 3 = 6 bags (Ans)

Test your child’s understanding by taking this short quiz!

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To Your Child’s Success,

Ms Nelly Ke
Math Specialist
Jimmy Maths and Grade Solution Learning Centre

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