Ali a acheté un roman et un dictionnaire de la langue française pour 350 dh . Si le prix du dictionnaire est supérieur de 80 dh au prix du roman, quel est le prix de chacun?

Let's denote the price of the book as \( x \) and the price of the dictionary as \( y \). Given that the total cost of the book and the dictionary is 350 dh, we can write the equation: \[ x + y = 350 \] Also, it is mentioned that the price of the dictionary is 80 dh more than the price of the book. Therefore, we can write another equation: \[ y = x + 80 \] Now, we have a system of two equations: \[ x + y = 350 \] \[ y = x + 80 \] We can solve this system of equations to find the prices of the book and the dictionary. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=350\\y=x+80\end{array}\right.\) - step1: Substitute the value of \(y:\) \(x+x+80=350\) - step2: Add the terms: \(2x+80=350\) - step3: Move the constant to the right side: \(2x=350-80\) - step4: Subtract the numbers: \(2x=270\) - step5: Divide both sides: \(\frac{2x}{2}=\frac{270}{2}\) - step6: Divide the numbers: \(x=135\) - step7: Substitute the value of \(x:\) \(y=135+80\) - step8: Calculate: \(y=215\) - step9: Calculate: \(\left\{ \begin{array}{l}x=135\\y=215\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=135\\y=215\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(135,215\right)\) The solution to the system of equations is \( x = 135 \) and \( y = 215 \). Therefore, the price of the book is 135 dh and the price of the dictionary is 215 dh.