Linear functions in word problems?

On Monday morning, she takes a taxi to the hospital, 7 km away. The ride costs €12.70. On Tuesday morning, she takes a taxi to the train station, 11 km away, and pays €18.70. Both rides were billed at the same fare. What is the base price on the taximeter at the start of the ride, and what is the price per kilometer?

How do you get 2.2 euros and 1.5km here?

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Dovahkiin11
6 years ago

Instead of presenting the solutions, I advise you to follow the procedure. Linear functions are of shape

y=ax+b

b is the starting value which is present at the beginning at x=0. It can also be 0 in such examples.

a is a gradient which is distinguished in the unit by a standardization at time/quantity/… These include €/Stk. , m/s , km/h, €/km …

x are variable times/quantities/… (unit which is in the denominator at a)

y is ultimately the sum of the km, €, … which is composed of the fixed initial value and the variable value. LGS are very often built up in this form, so that you can already read from the units how the equations look.

When it comes to apples and piece prices, maybe the total costs and the number of apples selected would be available, and you need to determine the price per apple. Or a total gasoline consumption and the number of kilometres traveled, from which you should determine the fuel price per kilometre.

In the task a is sought in €/km. The total costs are given in € and the variable distance in km.

Insert in the above form provides that Equation 1

b + 7km * a = 12,70 € a,b E R

b = start price, a = variable costs.

setting up the second equation and solution according to one of the known methods then provides the above-mentioned results.

Dovahkiin11
6 years ago
Reply to  Dovahkiin11

Thanks are overrated.

TrolltheMaster
6 years ago

7x+y=12,70

11x+y=18.70

and then you take a move

TrolltheMaster
6 years ago
Reply to  Bellejolie

is also easy, the km costs 1.5€, you can see the difference, 4 km to 6€

so start 2,20

Dovahkiin11
6 years ago
Reply to  TrolltheMaster

Presumably, the solutions are presented to him in such a way, very helpful.

TrolltheMaster
6 years ago
Reply to  Dovahkiin11

so I had understood this directly at an example task

I know very well, we had those with chickens and sheep

together x animals and number of legs

was very easy

Dovahkiin11
6 years ago

I’m glad you could do that, I’m afraid it’s not all like that. When the subject was discussed in our class a long time ago, the exceptions were.

Bellejolie, look at other tasks and try to understand how to get to the equations. You’ll have to do that in work. From your question I conclude that you have not been able to do this so far?