Question

Aki bought $ 3\dfrac{3}{4} $ pounds of spinach for \[ $ 6.88 \] . Using the unit rate, how much would $ 1\dfrac{1}{2} $ pounds of spinach cost?

Answer 1

Hint: To solve this question, we first have to find the unit rate. Unit rate means the rate of one pound of spinach. After this, we can get the cost for any quantity of the spinach by simply multiplying the unit rate with the given quantity.

Complete step by step solution:
We can see in the question that the quantity of spinach is given in the mixed friction form and the rate is given in the decimal form. Therefore, we will first convert both of them in the simple friction form.
 $ 3\dfrac{3}{4} = \dfrac{{4 \times 3 + 3}}{4} = \dfrac{{15}}{4} $ , $ 1\dfrac{1}{2} = \dfrac{{2 \times 1 + 1}}{2} = \dfrac{3}{2} $ and $ 6.88 = \dfrac{{688}}{{100}} $ .
Now, we will first find the unit rate.
We are given that the rate of $ 3\dfrac{3}{4} $ pounds of spinach is \[ $ 6.88 \] and we need to find the rate of one pound of spinach. Let us take the unit rate of spinach as \[ $ x \]

Quantity in pounds	Rate in $ \ $ $
$ \dfrac{{15}}{4} $	$ \dfrac{{688}}{{100}} $
$ 1 $	$ x $

 $ \Rightarrow x = \dfrac{{1 \times \dfrac{{688}}{{100}}}}{{\dfrac{{15}}{4}}} = \dfrac{4}{{15}} \times \dfrac{{688}}{{100}} \approx 1.83 = \dfrac{{183}}{{100}} $
Therefore, the unit rate of spinach is \[$ 1.83 \]= $ \dfrac{{183}}{{100}} $ .
Now, let us consider that the cost of $ 1\dfrac{1}{2} $ pounds of spinach is $ \ $ y $ .

Quantity in pounds	Rate in $ \ $ $
$ 1 $	$ \dfrac{{183}}{{100}} $
$ \dfrac{3}{2} $	$ y $

 $ \Rightarrow y = \dfrac{3}{2} \times \dfrac{{183}}{{100}} = 2.75 $
Hence, our final answer is: The cost of $ 1\dfrac{1}{2} $ pounds of spinach is \[ $ 2.75 \] .
So, the correct answer is “ \[ $ 2.75 \] .”.

Note: In this type of question, it is important to keep in mind that when the quantities or rates are given in the mixed fraction or decimal form, we need to convert them into simple fraction form. However, it can be calculated by converting all the numbers into decimal form also. But, to avoid complexity involved in decimal values, a simple fraction form can be used to make it quick and easy.