Answer

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**Hint:**In this problem we need to calculate the cost of the ball from the given data. In the given data we have costs of bat and ball and we don’t know both the values. So we will assume those values as variables say $x$ and $y$. In the problem we have the sum of the bat and ball cost as $\$1.10$. From this statement we can have an equation in terms of $x$ and $y$. They have also mentioned that the bat costs $\$1.00$ more than the ball. From this statement also we can have an equation in terms of $x$ and $y$. Now we will solve both the equations to get the costs of ball and bat.

**Complete step by step solution:**

Let us assume that,

The cost of the bat is $\$x$.

The cost of the ball is $\$y$.

Given that A bat and a ball cost $\$1.10$ in total. i.e., the sum of the cost of a bat and the cost of a ball us $\$1.10$. Mathematically we can write it as

$x+y=1.10....\left( \text{i} \right)$

In the problem, they have mentioned that The bat costs $\$1.00$ more than the ball. Mathematically we can write it as

$x=y+1...\left( \text{ii} \right)$

Substituting the above value in equation $\left( \text{i} \right)$, then we will have

$\begin{align}

& x+y=1.10 \\

& \Rightarrow y+1+y=1.10 \\

\end{align}$

Simplifying the above equation, then we will have

$\begin{align}

& \Rightarrow 2y+1=1.10 \\

& \Rightarrow 2y=1.10-1.00 \\

& \Rightarrow 2y=0.10 \\

& \Rightarrow y=\dfrac{0.10}{2} \\

& \therefore y=0.05 \\

\end{align}$

**Hence the cost of the ball is $\$0.05$.**

**Note:**In this problem they have only asked to calculate the cost of the ball only so we have calculated $y$ only. If they have also asked to calculate the cost of the bat then we will calculate the value of $x$. For this we will substitute the value of $y$ in any of the equations we have.

Substituting the $y$ value in the equation $\left( \text{ii} \right)$, then we will get

$\begin{align}

& x=0.05+1 \\

& \Rightarrow x=1.05 \\

\end{align}$

Hence the cost of the bat is $\$1.05$.

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