Liz has three pieces of strings, 18cm, 20cm and 24 cm long. She wants to cut them up to produce smaller pieces of string that are all of the same length, with no string left over. Calculate the greatest length, in cm, in which the strings can be cut. 2. Helen is organising a party and she needs party plates and straws. There are 30 party plates in a pack. There are 120 straws in a pack. She needs exactly the same number of plates as straws. Find the minimum number of each pack she must buy.

Question

08-10-2024
Mathematics

High School

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Liz has three pieces of strings, 18cm, 20cm and 24 cm long. She wants to cut them up to produce smaller pieces of string that are all of the same length, with no string left over. Calculate the greatest length, in cm, in which the strings can be cut. 2. Helen is organising a party and she needs party plates and straws. There are 30 party plates in a pack. There are 120 straws in a pack. She needs exactly the same number of plates as straws. Find the minimum number of each pack she must buy.

Answer :

Final answer:

Liz can cut each of her strings into pieces of 2 cm length. For the party, Helen needs to buy 4 packs of plates and 1 pack of straws to have an equal number of both items.

Explanation:

The subject of this question is Mathematics and it is at a Middle School grade level. The question contains two problems. For the first problem, Liz needs to find the greatest length to which she can cut her strings so that all pieces are equal. The greatest length in cm is determined by finding the Greatest Common Divisor (GCD) of the lengths of the three strings which are 18cm, 20cm, and 24cm. The GCD of these numbers is 2cm, so Liz can cut each string into pieces of 2 cm length.

For the second problem, Helen needs to organize a party with an equal number of plates and straws. She can buy packs of 30 plates and 120 straws. To ensure an equal number of plates and straws, she should buy 4 packs of plates and 1 pack of straws, which will give her a total of 120 plates and 120 straws.

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Answer :

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