Javid travels to work by bus or by train.

The daily bus fare is £2.50
The daily train fare is £3.50
In 5 days he spends a total of £14.50

On how many days did he travel by bus?

Respuesta :

Javid travelled by bus for 3 days using a simultaneous equation

What is simultaneous equation?

This refers to equations that are solved together in order to determine the values of unknown variables.

In this case, the total amount spent on daily bus or train can be determined as the fare price multiplied by the number of days

Let  X be the number of days that Javid took bus

total spent on bus=2.50X

Let Y be the number of days that Javid took train

total spent on train=3.50Y

Total spent=2.50X+3.50Y

14.50=2.50X+3.50Y

Secondly, X plus Y gives 5 days

5=X+Y

multiply the second equation by 2.50 and the first by 1

14.50=2.50X+3.50Y

12.50=2.50X+2.50Y

subtract the second equation from first

2=Y

substitute for Y

5=X+Y

5=X+2

X=5-2

X=3

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The number of days that he travelled by bus is; 3 days

How to Solve Simultaneous Equations?

Let  x be the number of days that Javid travelled by bus.

Let y be the number of days that Javid travelled by train.

Thus;

Total spent on bus = 2.50x

Total spent on train = 3.50y

Overall total spent is;

2.5x + 3.5y = 14.50   -----(1)

Total number of days is 5 days and so;

x + y = 5    -----(2)

Making x the subject in eq 2 gives us;

x = 5 - y     -----(3)

Put eq 3 in eq 1 to get;

2.5(5 - y) + 3.5y = 14.50

12.5 - 2.5y + 3.5y = 14.5

y = 14.5 - 12.5

y = 2 days

Thus;

x = 5 - 2

x = 3 days

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