Question

please help with question 20! thank you. it’s similar to a previous question i asked but i’m still not too sure how to approach it. thank you.

Answer 1

118

Explanation:

We are told that there are about 120 fruits.

Fruits divided equally among 4 students

Multiples of 4: 4, 8, 12, ... 112, 116, 120, 124, ...

Therefore, 116, 120 and 124 are closest to 120.

Add the given remainder of 2 to these numbers:

• 116 + 2 = 118
• 120 + 2 = 122
• 124 + 2 = 126

Fruits divided equally among 6 students

Multiples of 6: 6, 12, 18, ... 108, 114, 120, 126 ...

Therefore, 114, 120 and 126 are closest to 120.

Add the given remainder of 4 to these numbers:

• 114 + 4 = 118
• 120 + 4 = 124
• 126 + 4 = 130

Fruits divided equally among 15 students

Multiples of 15: 15, 30, 45, ... 105, 120, 135, ...

Therefore, 105, 120 and 135 are closest to 120.

Add the given remainder of 13 to these numbers:

• 105 + 13 = 118
• 120 + 13 = 133
• 135 + 13 = 148

Therefore, as the total of 118 fruits is common to all three groups the exact number of fruits is 118.

Check

Divide 118 by each group of students:

• 118 ÷ 4 = 29 r 2
• 118 ÷ 6 = 19 r 4
• 118 ÷ 15 = 7 r 13

As the remainders concur with the given amount of fruit left over for each group of students, this verifies that the exact number of fruits is 118.

Answer 2

118

Explanation:

The key piece of information to focus on is that there are around 120 fruits. 15 is the biggest of the given divisors, and the gaps between multiples of 15 is the greatest (compared to 4 and 6) which will narrow down our options. Therefore we can first try approaching the problem by finding multiples of 15 that are close to 120.

The question says that when the number (let's call it A) is divided by 15, it leaves 13. Therefore we can express A as such:

A-13 = 15x OR 15x + 13 = A

Where 'x' represents a whole number showing that the number is divisible by 15.

The closest multiples of 15 to 120 are 105 (15*7), 120 (15*8), and 135 (15*9).

A is one of these numbers + 13, let's see which ones are closest:

105+13 = 118, 120+13 = 133, 135+13 = 148

118 is very close to 120, so let's check it with the other numbers:

118/4 = 29 r 2

118/6 = 19 r 4

The exact number of fruits is 118.

Hope this helped!