Proportion word problem (example 2) | 7th grade | Khan Academy

TL;DR

Mika wants to know how long it would take her to eat 35 hot dogs if she can keep up the same pace as eating 21 hot dogs in 66 minutes.

Transcript

• We're told that Mika can eat 21 hot dogs in 66 minutes. She wants to know how many minutes, m, would it take her to eat 35 hot dogs, if she can keep up the same pace. So, big clue is the same pace, I have to remove a hair from my tongue, alright. (laughs) A big clue is the same pace. That means that the hot dogs, hot dogs per minute, per minute, ... Read More

Key Insights

• 😅 The eating pace, measured in hot dogs per minute, remains constant.
• 😫 A proportional relationship can be set up to solve the problem.
• ✖️ By multiplying both sides of the equation by the reciprocal of the coefficient on m, the equation can be simplified.
• 🥺 There are multiple ways to approach and solve this problem, leading to the same answer.
• 🥳 Understanding ratios and proportions is important in solving this type of problem.
• 🌭 The concept of minutes per hot dog can also be used to solve the problem.
• 🥺 Setting up an equation and using basic algebraic operations can lead to finding the unknown value.

Questions & Answers

Q: What is the key clue in determining the solution to this problem?

The key clue is that Mika's eating pace, measured in hot dogs per minute, remains constant.

Q: How can the ratio of hot dogs per minute be used to find the solution?

By setting up a proportional relationship, where 21 hot dogs in 66 minutes is equivalent to 35 hot dogs in m minutes, the value of m can be determined.

Q: How can the equation be simplified to solve for m?

By multiplying both sides of the equation by m, the m in the denominator can be eliminated, leaving a simple equation to solve for m.

Q: What is the final solution for m?

The final solution is m = 110 minutes, meaning it would take Mika 110 minutes to eat 35 hot dogs at the same pace.

Summary & Key Takeaways

• Mika can eat 21 hot dogs in 66 minutes at a constant pace.

• Her hot dogs per minute ratio is 21 hot dogs in 66 minutes.

• To calculate how long it would take her to eat 35 hot dogs, the same ratio can be applied.