Question

Half of Ethan's string is equal to 2/3 of Kayla's string. The total length of their strings is 10 feet. How much longer is Ethan's string than Kayla's? Drawing

Answer 1

Ethan's string is
`=(10)/(7)` feet longer than Kayla's string.

Explanation:

Let Ethan's string = x feet

and Kayla's string = y feet

According to question,

Half of Ethan's string is equal to 2/3 of Kayla's string that is,

`(1)/(2)x=(2)/(3)y`

`\Rightarrow x=(4)/(3)y` ..............(1)

Also,The total length of their strings is 10 feet that is,

`x+y=10`

Put value of x from (1),

`(4)/(3)y+y=10`

Solving for y, we get,

`\Rightarrow y((4)/(3)+1)=10`

`\Rightarrow y((4+3)/(3))=10`

`\Rightarrow y((7)/(3))=10`

`\Rightarrow y=(10 * 3)/(7)`

`\Rightarrow y=(30)/(7)`

Thus, Length of Kayla's string is
`(30)/(7)` feet.

and Put value of y in (1) to get value of x,

`\Rightarrow x=(4)/(3) * (30)/(7)`

`\Rightarrow x=(40)/(7)`

Thus, Length of Ethan's string is
`(40)/(7)` feet.

Length of Ethan's string is longer than Kayla's string = Length of Ethan's string-Length of Kayla's string.

`=(40)/(7)-(30)/(7)`

`=(10)/(7)`

Thus, Ethan's string is
`=(10)/(7)` feet longer than Kayla's string.

Answer 2

Answer:
`(10)/(7)` meters

Explanation:

Let x be the length of Kaya's string and y be the length of Ethan's string

Then According to the question, we have the following equations

`(1)/(2)y=(2)/(3)x\\\Rightarrow\ y=(4)/(3)x......(1)\\x+y=10....(2)`

Substitute the value of y from (1) in (2), we get

`(4)/(3)x+x=10\\\Rightarrow(4x+3x)/(3)=10\\\Rightarrow\ (7x)/(3)=10\\\Rightarrow\ x=(30)/(7)`

The length of Kaya's string =
`(30)/(7)` feet

The length of Ethan's string =
`(4)/(3)*(30)/(7)=(40)/(7)` meters

The difference in their lengths=
`(40)/(7)-(30)/(7)=(10)/(7)`

Hence, Ethan's string is
`(10)/(7)` meters longer than the Kaya's string.