Question

Sally buys \[2\dfrac{1}{2}\] pounds of bananas for \[\$1.50\]. How much is she paying for one pound of bananas?

Answer 1

Hint: This question is from the topic of algebra. In this question, we have to find the price for one pound of bananas. In solving this question, we will first find the ratio of weight of bananas to the price of bananas for the same weight. After that, we will take a variable x as the price of bananas that we have to find. So, using the ratio and 1 pound, we will find the value of x and get our answer.

Complete step-by-step solution:
Let us solve this question.
In this question, we have given that Sally buys \[2\dfrac{1}{2}\] pounds of bananas for which she has to pay \[\$1.50\]. So, we have to find what will be the money for one pound of bananas.
We will first convert the mixed number that is \[2\dfrac{1}{2}\] to the improper fraction or improper number.
We can write
\[2\dfrac{1}{2}=\dfrac{2\times 2+1}{2}\]
The above can also be written as
\[\Rightarrow 2\dfrac{1}{2}=\dfrac{4+1}{2}\]
The above can also be written as
\[\Rightarrow 2\dfrac{1}{2}=\dfrac{5}{2}\]
We can see that for \[2\dfrac{1}{2}\] pounds of bananas, the price is \[\$1.50\]
Or, we can say for \[\dfrac{5}{2}\] pounds of bananas, the price is \[\$1.50\]
Now, we will find out the ratio of weight of bananas to the price of bananas.
\[\text{Ratio}=\dfrac{\text{Weight of bananas(in pounds)}}{\text{Price of bananas(in }\!\!\$\!\!\text{)}}=\dfrac{\dfrac{5}{2}}{1.50}\]
The above can also be written as
\[\Rightarrow \dfrac{\text{Weight of bananas(in pounds)}}{\text{Price of bananas(in }\!\!\$\!\!\text{)}}=\dfrac{5}{2\times1.50}\]
The above can also be written as
\[\Rightarrow \dfrac{\text{Weight of bananas(in pounds)}}{\text{Price of bananas(in }\!\!\$\!\!\text{)}}=\dfrac{5}{3}\]
Now, let us take the price for one pound of bananas as x (which is in \[\$\]). Then, we can write
\[\Rightarrow \dfrac{1}{x}=\dfrac{5}{3}\]
The above can also be written as
\[\Rightarrow x=\dfrac{3}{5}\]
\[\Rightarrow x=0.6\]
Hence, we can say that Sally is paying \[\$0.60\] for one pound of bananas.

Note: As this question is from the topic of algebra, we should have a better knowledge in that topic. We should know how to convert a mixed number into an improper fraction or improper number. Let us understand this by the following:
Let us suppose the mixed number is \[x\dfrac{y}{z}\]. Here, x is the whole number, y is numerator and z is denominator.
Now, for converting into an improper fraction, we will multiply the whole number by denominator and then add with numerator. The resultant will be written in numerator and denominator will be the same.
So, we can write \[x\dfrac{y}{z}\] as
\[x\dfrac{y}{z}=\dfrac{x\times y+z}{z}\]
Hence, the improper fraction of mixed numbers \[x\dfrac{y}{z}\] will be \[\dfrac{x\times y+z}{z}\].