Tiffany is sending a package that may not exceed 16 pounds. The package contains books that weigh a total of 9 3/8 pounds.The other items to be sent weigh 3/5 of the books.Will Tiffany be able to send the package? Show your work.

Feb 22, 2018

Yes, Tiffany will be able to send the package, as it will weigh 15 pounds.

Explanation:

$9 \frac{3}{8} = \frac{9 \cdot 8 + 3}{8} = \frac{75}{8}$

The other items weigh $\frac{3}{5}$ what the books weigh, so we multiply as follows:

$\frac{75}{8} \cdot \frac{3}{5} = \frac{225}{40} = 5 \frac{25}{40}$ which simplifies to $5 \frac{5}{8}$.

We then add $9 \frac{3}{8} + 5 \frac{5}{8} = 14 \frac{8}{8} = 15$

Therefore, the total weight of the package will be 15 pounds, which is 1 pound less than the maximum weight she can send.

Feb 22, 2018

The parcel will weight $15$ pounds so she can send it.

Explanation:

You can do this with one calculation if you realise that you need to increase $9 \frac{3}{8}$ by $\frac{3}{5}$ of its weight.

The new weight will be $1 + \frac{3}{5} = 1 \frac{3}{5}$ of the original weight.

$9 \frac{3}{8} \times 1 \frac{3}{5}$ will give the increased weight.

$= \frac{75}{8} \times \frac{8}{5}$

$= {\cancel{75}}^{15} / \cancel{8} \times \frac{\cancel{8}}{\cancel{5}} ^ 1$

$= 15$ pounds

As the maximum weight is $16$ pounds, Tiffany will be able to send the parce.