Question

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

Answer 1

The answer is 4 3/4 yards of the fabric.

Answer 2

The answer is 4 3/4 yards of the fabric.

This can be calculated using the proportion.
If the 3 1/6 yards of the fabric is enough for 1 1/3 shirts, how many yards are necessary of 2 shirts:

`3 (1)/(6) yards :1 (1)/(3)shirts =xyards:2shirts`

Let's express 3 1/6 as 19/6:

`3 (1)/(6) =3+ (1)/(6) = 3* (6)/(6)+ (1)/(6) = (18)/(6) + (1)/(6) = (18+1)/(6) = (19)/(6)`

Similarly, 1 1/3 = 4/3:

`1 (1)/(3) =1+ (1)/(3) = 1* (3)/(3)+ (1)/(3) = (3)/(3) + (1)/(3) = (3+1)/(3) = (4)/(3)<span>`

Now, let's use this in the proportion:

`3 (1)/(6) yards :1 (1)/(3)shirts =xyards:2shirts`

`(19)/(6) : (4)/(3) = x:2`

Crossing the products:

`x* (4)/(3) =2* (19)/(6)`
⇒
`x* (4)/(3) = (19)/(3)`
⇒
`x = (19)/(3) : (4)/(3)`

`x= (19)/(3) * (3)/(4)`
⇒
`x = (19)/(4) = (16+3)/(4) = (16)/(4) + (3)/(4) =4+ (3)/(4) =4 (3)/(4)`

Therefore, Mary needs in total 4 3/4 yards of the fabric.