Question

$2\dfrac{1}{4}$ ton equals how many pounds?

Answer 1

Hint: To solve this question, we first need to convert the value $2\dfrac{1}{4}$ which is in mixed fraction to the improper fraction. After converting, we will get it as $\dfrac{9}{4}$ ton. Then we need to convert it into equivalent amount in pounds. For this we have to use the conversion of amount of tonnes in one pound, which is given by $\text{lb}=\text{T}\times 2204.6$. Finally on substituting $\dfrac{9}{4}$ tonnes in this conversion, we will get the required equivalent amount in pounds.

Complete step-by-step answer:
We know that one ton is equivalent to $2204.6$ pounds. Therefore, we can write
$\Rightarrow 1\text{T}=2204.6\text{lb}$
By using the unitary method, we can say that for converting a given amount from tonnes to pounds, we need to multiply that amount by the number $2204.6$. From this information, we can write the standard conversion equation as below.
\[\Rightarrow \text{lb}=2204.6\text{T}.....\left( i \right)\]
Now, according to the information given in the above question, we have $2\dfrac{1}{4}$ tonnes. This value is given in the mixed fraction. We can write it in the improper fraction as $\dfrac{4\times 2+1}{4}$ which is equal to $\dfrac{9}{4}$ tonnes. Putting this value in tonnes in the above conversion equation (i), we get
\[\Rightarrow \text{lb}=2204.6\times \dfrac{9}{4}\]
On solving the above expression, we finally get
\[\Rightarrow \text{lb}=4960.35\]
Thus, the equivalent amount in which we got is equal to \[4960.35\] pounds.
Hence, $2\dfrac{1}{4}$ ton is equal to \[4960.35\] pounds.

Note: Do not misread the conversion equation, which is obtained in the above solution as $\text{lb}=\text{T}\times 2204.6$, as equivalent amount in tonnes of one pound. On the LHS, only the symbol of pound is written which refers to the equivalent amount in tonnes. Also, do not misread the amount $2\dfrac{1}{4}$ ton as $\dfrac{21}{4}$ ton.