write an equation to represent the following equation: 60 is 5 times as great as k solve for k
The correct answer and explanation is:
Correct Answer:
The equation that represents the statement “60 is 5 times as great as k” is: 60=5k60 = 5k
To solve for k, divide both sides of the equation by 5: k=605=12k = \frac{60}{5} = 12
300-Word Explanation:
The statement “60 is 5 times as great as k” is a comparison that can be translated into a mathematical equation. Let’s break it down:
- The number 60 is being compared to k.
- The phrase “5 times as great as k” means that you multiply k by 5.
- So, we can say that 60 equals 5 multiplied by k, which gives us the equation:
60=5k60 = 5k
This is a linear equation where k is the unknown variable. The goal is to isolate k on one side of the equation so we can find its value.
To isolate k, divide both sides of the equation by 5: 605=5k5\frac{60}{5} = \frac{5k}{5} 12=k12 = k
Thus, k = 12.
Understanding the Logic:
Translating word problems into equations is a key skill in algebra. Key phrases help with this process:
- “Is” typically means equals (=).
- “Times” indicates multiplication.
- “As great as” means we are comparing two quantities.
In this case, the structure is:
[Known number] = [Multiplier] × [Unknown]
Which is:
60 = 5 × k
By solving, we discover that k must be 12, because 5 multiplied by 12 gives us 60.
This problem demonstrates how algebra allows us to find unknown values using logical relationships described in words.