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So let's draw this garden here, Tina's garden. So if this is the width, then this is also going to be the width. And they tell us that the length of the garden is twice the width.
Before you start solving word problems in algebra, you should first already know about real numbers, how to manipulate algebraic expressions, and how to solve math problems involving linear equations and inequalities.
We will focus on application of these concepts through word problems.
We will call the smaller integer n, and so the larger integer must be n 2 And we are told the product (what we get after multiplying) is 168, so we know: n(n 2) = 168 We are being asked for the integers Solve: That is a Quadratic Equation, and there are many ways to solve it.
Using the Quadratic Equation Solver we get −14 and 12.
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If you're behind a web filter, please make sure that the domains *.and *.are unblocked.We know there are seven days in the week, so: d e = 7 And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d 3e = 27 We are being asked for how many days she trains for 5 hours: d Solve: The number of "5 hour" days is 3 Check: She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours So Joel’s normal rate of pay is per hour Check Joel’s normal rate of pay is per hour, so his overtime rate is 1¼ × per hour = per hour.This problem illustrates the process of unit conversion; a year is the same as 525,600 minutes even though 1 ≠ 525,600.Bill takes a trip in which he drives a third of the time at 30 miles per hour, a third of the time at 50 miles per hour, and a third of the time at 70 miles per hour.The perimeter of Tina's rectangular garden is 60 feet. So if this is w, then the length is going to be 2w. If the length of the garden is twice the width, what are the dimensions of the garden? Check −14: −14(−14 2) = (−14)×(−12) = 168 YES Check 12: 12(12 2) = 12×14 = 168 YES So there are two solutions: -14 and -12 is one, 12 and 14 is the other.Note: we could have also tried "guess and check": And so L = 8 or −14 There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!We know that we can find the distance traveled by multiplying the speed and the time traveled at that speed (for instance, if we travel 2 hours at 30 miles per hour, we have gone 60 miles).In addition, we know that Bill travels a third of the time ( The Celsius (C) and Fahrenheit (F) temperature scales are related by a linear function.