Solving Linear Equations Word Problems Worksheet
The ages of Jaspreet and Dharam differ by 30 years. Hint: Case -1 $x - y =3$ x - \frac = 30$ (19,16) Case -2 $y - x =3$ x - \frac = 30$ ( 21,24) Question 6 A takes 3 hours more than B to walk 30 km. Manjit's father Dharam is twice as old as Manjit and Ranjit as twice as old as his sister Jaspreet.Find the distance covered by the man and his original rate of walking.Hint: Let v = the rate the man walked, t=time taken originally and d=distance $d=vt$ Case 1 (faster) Speed= (v .5) time=(t-1) = time taken at the faster speed Now $distance = velocity \times time$ $vt= (v .5)(t-1)$ $v - .5t = -.5$ (1) Case 2 (slower) speed=(v-1) time=(t 3) Now $distance = velocity \times time$ $vt = (v-1)(t 3)$ $-3v t = -3$ (2) Solving (1) and (2) v=4 km/hr ,t=9 hr, hence d= 36 km Question 10 Anuj travels 600 km partly by train and partly by car.Hint: Let speed of boat in still water be x km/h and speed of stream be y km/h.Speed upstream= (x - y) km/h Speed downstream= (x y) km/h $\frac \frac = 10$ $\frac \frac = 13$ Now Substituting $p=\frac $ and $q=\frac $,then solving p=1/5 and q=1/11 Hence $x-y=5$ and $x y =11$, Solving these, x=8 km/hr and y=3km/hr Question 8 A boat goes 24 km upstream and 28 km downstream in 6 hrs.Just as "26" is "10 times 2, plus 6 times 1", so also the two-digit number they've given me will be ten times the "tens" digit, plus one times the "units" digit.
If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. First thing we have to do in this assignment is to find the variable and see what its connection is with the other values. 4 * x 10 = 30 Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation.It can go 16 km upstream and 32 km downstream in the same time.Find the speed of the boat in still water and the speed of the stream.This is one reason why linear algebra (the study of linear systems and related concepts) is its own branch of mathematics.In your studies, however, you will generally be faced with much simpler problems. The ten's digit stands for "ten times of this digit's value".These word problems are called two-step because you have to perform two mathematical operations in order to solve them.In this case – addition (subtraction) and multiplication (division).But if you feel ready, we will show you how to solve it using this example: Hermione’s Bikes rents bikes for plus per hour. The thing we do not know is the number of hours Janice rented the bike for and we have been asked to find that out. The cost of renting a bike is 10$ to take the bike and 4$ for every hour it spends in our possession. Like this: 4 * x = 30 – 10 To simplify things further, let us perform the subtraction.4 * x = 20 The next thing to do is to get rid of the number 4 in front of the variable.Plugging the three points in the general equation for a quadratic, I get a system of three equations, where the variables stand for the unknown coefficients of that quadratic: ..other conics, though parabolas are the most common.Keep in mind that projectile problems (like shooting an arrow up in the air or dropping a penny from the roof of a tall building) are also parabola problems, using: if you're working in feet).