Question

Choose the word phrase (greater than, less than, or equal to) to make the statements true.

Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.

Twelve matches are worth
two pencils and one paper clip

Answer 1

Five pencils and two marches are worth greater than thirty paper clips.

Explanation:

Let 'x' be paper clip.

Let 'y' be a match

and let 'z' be a pencil.

Now, let's write each statement as an equation:

Each paper clip can be traded for three matches:

x = 3y

Each pencil can be traded for six paper clips:

z = 6x

Now, five pencils equals 30 paper clips and two matches equals two thirds papel clips.

Therefore, we can say that Five pencils and two matches equals 30.66 matches. Therefore, five pencils and two marches are worth greater than thirty paper clips.

Answer 2

less than

Explanation:

Let x be the worth of a match.

Each paper clip can be traded for three matches. It means the worth of a paper clip is 3 times of the worth of a match.

Worth of a paper = 3x

Each pencil can be traded for six paper clips. It means the worth of a pencil is 6 times of the worth of a paper clip.

Worth of a pencil = 6(3x) =18x

The worth of a match, a paper and pencil are x, 3x and 18x respectively.

Worth of Twelve matches = 12 × x = 12x

Worth of two pencils and one paper clip = 2(18x) + 1(3x) = 39x

It is clear that

`12x<39x`

because,

`12<39`

Therefore, the twelve matches are worth less than two pencils and one paper clip.