Question

Jim, Sashi, and Anuj had a pizza which cost Rs.110 in a fast-food restaurant. Sashi did not eat as much as his friends. So they decided that Sashi should pay half of what the other two paid. How much should Sashi pay? \[\]

Answer 1

Hint: We assume the amount paid by Jim as $ x $ rupees, the amount paid by Sashi as $ y $ rupees, and the amount paid by Anuj as $ z $ rupees. We use the given that Sashi should pay half of what the other two paid and express $ x,z $ in terms of $ y $ . We make the equation $ x+y+z=110 $ and put $ x,z $ in terms of $ y $ in the equation and solve for $ y $ . \[\]

Complete step by step answer:
Let us assume the amount paid by Jim as $ x $ rupees, the amount paid by Sashi as $ y $ rupees, and the amount paid by Anuj as $ z $ rupees. We give in the question that Jim, Sashi, and Anuj paid a total cost of Rs.110 in the fast-food restaurant which means the sum of the cost paid by Jim, Sashi and Anuj separately is Rs.110. So we have;
\[x+y+z=110......\left( 1 \right)\]
We are further given in the question that Sashi did not eat as much as his friends. So they decided that Sashi should pay half of what the other two paid. We know that in a restaurant bill is shared equally among friends which means is Sashi would have eaten equally as his friends the bill would have been equally shared by the three friends which means $ x=z $ \[\].
 Since has to pay half of what Jim pave we have;
\[y=\dfrac{x}{2}\]
We multiply 2 both side to have;
\[\Rightarrow x=2y.......\left( 2 \right)\]
Since Sashi also pays half of what Anuj paid we have;
\[y=\dfrac{z}{2}\]
 We multiply 2 both side to have;
\[\Rightarrow z=2y...\left( 3 \right)\]
We put the values of $ x $ and $ z $ from (2) and (3) and put them in equation (1) to have;

\[\begin{align}
  & \Rightarrow 2y+y+2y=110. \\
 & \Rightarrow 5y=110 \\
\end{align}\]
We divide both sides of the above equation by 5 to have;
\[\Rightarrow y=22\]
So Shashi should pay 22 rupees. \[\]

Note:
 We note that the question is ambiguous in the phrase ‘Sashi should pay half of what the other two paid’ because it can also mean $ y=\dfrac{x+z}{2} $ . The obtained equation in $ y $ that is $ 5y=110 $ is a linear equation in one variable. We solve it by separating the variables and constant at two different sides of the equation.