Question

Susan bought `2 3/4` pounds of potato salad at $5.60 a pound. How much did she spend?

Answer 1

See a solution process below:

Explanation:

The formula for solving this problem is:

`c = p xx a` Where:

`c` is the total cost, what we will be solving for

`p` is the price of the item, `($5.60)/(lb)` for this problem.

`a` is the amount purchased. `2 3/4 lb` for this problem.

Substituting gives:

`c = ($5.60)/(lb) xx 2 3/4 lb`

First, we can cancel common terms:

`c = ($5.60)/color(red)(cancel(color(black)(lb))) xx 2 3/4 color(red)(cancel(color(black)(lb)))`

`c = $5.60 xx 2 3/4`

Next, we can convert the mixed fraction to an improper fraction:

`c = $5.60 xx (2 + 3/4)`

`c = $5.60 xx ((4/4 xx 2) + 3/4)`

`c = $5.60 xx (8/4 + 3/4)`

`c = $5.60 xx 11/4`

Now, we can multiply the two terms to calculate `c`:

`c = ($61.60)/4`

`c = $15.40`

Susan spent $15.40

Answer 2

Susan spent `2 3/4 \times $5.60=$11/4\times 56/10=$(11\times 14)/10=$ 15.40`.

Explanation:

The question is meant to test how well you can convert between all sorts of ways to represent fractions.

We start off by converting everything to improper fractions.

`2 3/4=2 + 3/4=(2\times 4 + 3)/4=(8 + 3)/4=11/4`

Hence, we have `11/4` pounds of potato salad.

Now, `$5.60=$560/100=$56/10`

(Note that we could simplify the fraction even further at this point, but since we are going to do that at the end anyway, we decide to keep the `10` in the denominator for ease of calculation)

Then comes a simple application of the Unitary Method:

`1` pound of potato salad costs `$56/10`
Therefore, `11/4` pounds of potato salad costs `$11/4 \times 56/10=$ (11 \times 14)/10=$154/10=$15.40`.

(We cancel `56` by `4` to get `14`. Then we multiply `11` by `14` to get `154`. Finally we divide by `10` and write the answer with `2` places of decimal, as we normally do for units of currency)

Note : All the calculations can also be done by converting everything to decimals, but more often than not, the methods becomes cumbersome and lengthy. Also, you may encounter non-terminating fractions like `1/3`. Therefore, it is recommended to convert everything to improper fractions and perform short and easy calculations as and when necessary.