Question

To sew a garment, a seamstress uses 5.7 centimeters of thread for every 7.6 centimeters of fabric.

a) If the seamstress uses 4.2 centimeters of thread, how much fabric is involved?
b) If the seamstress is working with 21.2 centimeters of fabric, how many centimeters of thread is needed?
c) Explain how you found your answers and show your work.

Answer 1

a) Since,
`\text{ 5.7 cm of thread} = \text{ 7.6 cm of fabric}`

⇒
`\text{ 1 cm of thread} = (7.6)/(5.7)\text{ cm of fabric}`

⇒
`\text{ 4.2 cm of thread} =(7.6)/(5.7)* 4.2\text{ cm of fabric}`

⇒
`\text{ 4.2 cm of thread} =(31.92)/(5.7)\text{ cm of fabric}`

⇒
`\text{ 4.2 cm of thread} =5.6\text{ cm of fabric}`

Therefore, For 4.2 cm of thread, 5.6 cm of fabric involved.

b) Again,

`7.6\text{ cm of fabric} = 5.7\text{ cm of thread}`

⇒
`1\text{ cm of fabric} = (5.7)/(7.6)\text{ cm of thread}`

⇒
`21.2\text{ cm of fabric} =(5.7)/(7.6)* 21.2\text{ cm of thread}`

⇒
`21.2\text{ cm of fabric} =(120.84)/(7.6)\text{ cm of thread}`

⇒
`21.2\text{ cm of fabric} =15.9\text{ cm of thread}`

Therefore, For 21.2 cm of fabric, 15.9 cm of thread is used.