Question

A piece of blue yarn is 4 7
10
yards long. A piece of pink yarn is 6 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?

Answer 1

Given:

A piece of blue yarn is 4 7/10 yards long. A piece of pink yarn is 6 times as long as the blue yarn.

To find:

How much longer is the pink yarn than the blue yarn?

Solution:

The length of the blue yarn = $4\frac{7}{10}$ yards

we will convert this length into improper fraction from mixed fraction for easy calculations

i.e., $4\frac{7}{10}$ yards = $\frac{47}{10}$ yards

The piece of pink yarn is 6 times the blue yarn

So, we get

The length of the pink yarn is,

= 6 × [Length of the blue yarn]

= 6 × $\frac{47}{10}$

= $3 \times \frac{47}{5}$

= $\frac{141}{5}$ yards

Now,

The difference between the length of blue and pink yarn is,

= $\frac{141}{5 } - \frac{47}{10}$

= $\frac{282 - 47}{10}$

= $\frac{235}{10}$

= $\frac{47}{2}$

converting into mixed fractions

= $\bold{23\frac{1}{2} \:yards}$

Thus, the pink yarn is $\bold{\underline{23\frac{1}{2} \:yards}}$ longer than the blue yarn.

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