In a kiosk, the total price of a chicken leg and a rice dumpling is $17.5. Four chicken legs are as expensive as three rice dumplings. How much should Ben pay for two rice dumpling... In a kiosk, the total price of a chicken leg and a rice dumpling is $17.5. Four chicken legs are as expensive as three rice dumplings. How much should Ben pay for two rice dumplings and a chicken leg? Read more

Steps to Solve

1. Define Variables Let ( x ) be the price of a rice dumpling and ( y ) be the price of a chicken leg.

2. Set Up the Equations From the problem statement, we can create two equations:

• The total price of a chicken leg and a rice dumpling: $$ x + y = 17.5 $$
• Four chicken legs are as expensive as three rice dumplings: $$ 4y = 3x $$

3. Rearranging the Second Equation From the second equation, solve for ( y ): $$ y = \frac{3}{4} x $$

4. Substituting ( y ) in the First Equation Substituting the expression for ( y ) from step 3 into the first equation: $$ x + \frac{3}{4} x = 17.5 $$ Combine the terms: $$ \frac{7}{4} x = 17.5 $$

5. Solve for ( x ) To find ( x ), multiply both sides by ( \frac{4}{7} ): $$ x = 17.5 \times \frac{4}{7} $$ Calculating: $$ x = 10 $$

6. Substituting ( x ) back to find ( y ) Now substitute ( x = 10 ) back into the equation for ( y ): $$ y = \frac{3}{4} \times 10 $$ Calculate: $$ y = 7.5 $$

7. Calculating Total for Ben's Purchase Ben wants 2 rice dumplings and 1 chicken leg: $$ \text{Total} = 2x + y = 2(10) + 7.5 = 20 + 7.5 = 27.5 $$