Mr. Mitchell drives 465 miles in 12 hours. Find the unit rate.
In this problem, students need to understand what the "unit rate" is. Unit rate is defined as a comparison of two different quantities where the second quantity is a unit of 1. With this being said, we need to write this rate in miles per 1 hour. To do this, we can divide 465 by 12. Our final answer would be 38.75 miles per hour.
14 is what percent of 56?
To solve this problem, we should set up a proportion. The proportion we can use for percents is the following: is/of = %/100. In this case, "14" refers to the "is" and "56" refers to the "of". The percent is unknown so we can use "x" to represent the percent. Our proportion would then look like the following: 14/56 = x/100 To solve this proportion, we can cross-multiply to solve. When we do that, we get: 1400 = 56x. This is now a 1 step equation. We can solve this by dividing each side by 56. When we do that, we get x = 25%.
Jimmy earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Jimmy worked both jobs for a total of 30 hours, and earned $690. How long did Jimmy work as a carpenter last week, and how long did he work as a blacksmith?
The first step to solving this word problem is to create a system of equations. We have two unknown quantities in this problem. We can call "x" the number of hours worked as a carpenter and "y" the number of hours worked as a blacksmith. Our first equation builds a relationship of the amount of money Jimmy made 20x + 25y = 690 The second equation builds a relationship of the total number of hours worked. x + y = 30 We now have a system of equations with the following two equations: 20x + 25y = 690 x + y = 30 We could solve this system by using elimination. First, we could multiply the bottom equation by -20. Our two equations will now be the following: 20x + 25y = 690 -20x + -20y = -600 We could then add the two equations together. When we do that, our new equation is: 5y = 90. This is now a one-step equation. We can solve this equation by dividing both sides by 5. Our solution is y = 18 hours. To find x, we can plug "18" in for "y" into either equation. x + y = 30 x + 18 = 30 To solve this one-step equation, we subtract 18 from both sides and get x = 12 hours. Our final answer is that Jimmy works 12 hours as a carpenter and 18 hours as a blacksmith.