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Video: Using Variables to Represent Numbers and Write Equations When Solving a Mathematical or Real-World Problem

Kathryn Kingham

Given that it costs $12 for each hour of snorkeling and that the cost of the equipment is $11, determine the equation that represents the cost in dollars, 𝑐, for snorkeling for โ„Ž hours.

02:31

Video Transcript

Given that it costs twelve dollars for each hour of snorkeling and that the cost of the equipment is eleven dollars, determine the equation that represents the cost in dollars, ๐‘, for snorkeling โ„Ž hours. What is the question asking us to do? What are we looking for here? The question is asking us for an equation: determine the equation that represents the cost in dollars for this problem.

Our question has given us two variables, ๐‘ for the cost in dollars and โ„Ž for the number of hours that someone went snorkeling. We know that it cost twelve dollars for each hour that youโ€™re snorkeling and that the cost of the equipment is eleven dollars.

This eleven dollars is something that we only pay once; we donโ€™t pay per hour. We have to pay the twelve dollars every hour that weโ€™re snorkeling.

Letโ€™s put all these pieces together into an equation. Weโ€™re trying to find the total cost. We know that the total cost is the cost of the equipment plus the cost of the time spent snorkeling. What we need to do now is replace each of these items with the mathematical representation of them.

Letโ€™s start with total cost. We donโ€™t know what the total cost is, but we know that our question has asked us to represent the cost in dollars with the variable ๐‘.

Next step, the equipment. The equipment costs eleven dollars, and it costs eleven dollars no matter if you spend one hour snorkeling or twenty hours snorkeling. So we just leave eleven as the cost of the equipment.

Finally, what is the cost of the time spent snorkeling? The cost of the time spent snorkeling is twelve dollars per hour; twelve times โ„Ž, where โ„Ž represents the number of hours you were snorkeling. Eleven plus twelve โ„Ž equals ๐‘.