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?
Understand the Problem
The question is asking for the cost Ben needs to pay for two rice dumplings and one chicken leg, given the total price of both items and the relationship between their prices. We will solve it by establishing a system of equations based on the information provided.
Answer
Ben should pay $27.5 for two rice dumplings and a chicken leg.
Answer for screen readers
Ben should pay $27.5 for two rice dumplings and one chicken leg.
Steps to Solve
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Define variables for prices Let the price of a chicken leg be $c$ and the price of a rice dumpling be $r$.
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Set up the first equation From the problem, we know the total price for one chicken leg and one rice dumpling: $$ c + r = 17.5 $$
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Set up the second equation The problem states that four chicken legs are as expensive as three rice dumplings, which can be expressed as: $$ 4c = 3r $$
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Rearrange the second equation Solving for $c$ in terms of $r$ gives: $$ c = \frac{3r}{4} $$
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Substitute into the first equation Now substitute $c$ from the rearranged equation into the first equation: $$ \frac{3r}{4} + r = 17.5 $$
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Combine like terms To combine the terms, convert $r$ into terms of quarters: $$ \frac{3r}{4} + \frac{4r}{4} = \frac{7r}{4} = 17.5 $$
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Solve for $r$ Multiply both sides by 4 to eliminate the fraction: $$ 7r = 70 $$ Now divide by 7: $$ r = 10 $$
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Substitute back to find $c$ Substitute $r$ back into the equation for $c$: $$ c = \frac{3(10)}{4} = 7.5 $$
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Calculate total cost for Ben Now compute the total cost for two rice dumplings and one chicken leg: $$ 2r + c = 2(10) + 7.5 = 20 + 7.5 = 27.5 $$
Ben should pay $27.5 for two rice dumplings and one chicken leg.
More Information
The prices we established show a clear relationship between the two items based on the given conditions. Awareness of how to set up equations from word problems is key in solving such problems.
Tips
- Not defining variables clearly: Always define variables to keep track of what each symbol represents.
- Mixing up the equations: Be careful to keep equations organized and ensure they reflect the problem's conditions accurately.
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