Solving Direct Variation Problems
If a gallon of gas costs .25, how many gallons could you purchase for ?
Now, they give us more information, and this will help us figure out what k is.
For the case given in the problem,180 = V × 3 or V = \(\frac\) = 60So speed of the car is 60kmph and it is constant.
For 100 km distance S = VT or 100 = 60 × TT = \(\frac\) = \(\frac\) hrs = 1 hr 40 mins. In X is in direct variation with square of Y and when X is 4, Y is 3.
This can be explained with a direct variation equation.
If T denotes total numbers scored, N denotes numbers of problem solved and K denotes numbers can be scored for solving a problem, then the direct variation equation for this situation will be T = KN.
The following statements are equivalent * y varies directly as x * y is directly proportional to x * y = kx for some constant k What is the direct variation formula?Graphically, we have a line that passes through the origin with the slope of k. If the distance is 10 cm when the mass is kg, what is the distance when the mass is 5 kg? We're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing. So if x is equal to 1-- this statement up here, a gallon of gas-- that tells us if we get 1 gallon, if x is equal to 1, then y is .25, right? They tell us 1 gallon costs .25, so you could write it right here, .25 is equal to k times x, times 1. So the equation, how y varies with x, is y is equal to 2.25x, where x is the number of gallons we purchase. Now if we want to solve for x, we can divide both sides by 2.25, so let's do that. So first of all, I just like to think of it as a fraction.Solution: As P varies directly with Q, ratio of P and Q is constant for any value of P and Q.So constant K = \(\frac\) = \(\frac\) = \(\frac\)So the equation that describes the direct variation of P and Q is P = \(\frac\)Q. There are many situations in our daily lives that involve direct variation.The two quantities = 55.42 The cost for 95 km is .42 How to define direct variation and solve direct variation word problems?This is symbolically written as, A ∝ B (read as, ‘A varies as B’ ).Like in a math examination if for one problem solving we can score 10 numbers, so five problems solving we can get 50 numbers.Direct variation can be by a linear equation Y = KX where K is a constant.When the value of constant is higher, the change of variable Y is significantly for small change of X.