Question

In a city, 70% of commuters use the subway/bus to get to work, 50% use taxis/Uber and 20% use exclusively their own car. If 596,500 commuters use both subway/bus and taxi/Uber, how many commuters are in the city? Solve the problem by first formulating an equation.

Answer 1

To solve the problem, we can set up an equation. We know the percentages of commuters using different modes of transportation and the number of commuters using both subway/bus and taxi/Uber. However, the resulting equation yields a negative number of commuters, indicating an error in the problem or given information.

Step-by-step explanation:

To solve this problem, we can start by setting up an equation.

Let's assume that the total number of commuters in the city is represented by 'x'.

From the given information, we know that 70% of commuters use the subway/bus, which is 0.7x.

We also know that 50% use taxis/Uber, which is 0.5x.

And 20% use exclusively their own car, which is 0.2x.

Since 596,500 commuters use both the subway/bus and taxi/Uber, we can subtract this double-counted group from the total number of commuters.

Therefore, the equation is:

x - 0.7x - 0.5x + 596,500 = 0

Simplifying the equation, we get:

0.2x + 596,500 = 0

Subtracting 596,500 from both sides, we have:

0.2x = -596,500

Dividing both sides by 0.2, we get:

x = -596,500 / 0.2

Calculating this, we find that the total number of commuters in the city is -2,982,500.

However, it is not possible to have negative commuters, so we can conclude that there was an error in the problem or the given information.

Answer 2

To find the total number of commuters in the city, set up an equation using the given percentages and the number of commuters who use both subway/bus and taxi/Uber. By solving this equation, we determine that the total number of commuters is 2,982,500.

Step-by-step explanation:

To solve this problem, we need to set up an equation based on the percentages given and the actual number of commuters who use both subway/bus and taxi/Uber. We are told that 70% of commuters use the subway/bus, 50% use taxis/Uber, and 20% use exclusively their own car. Additionally, 596,500 commuters use both subway/bus and taxi/Uber. We should note that the sum of percentages exceeds 100%, which means there is an overlap where commuters use more than one type of transportation.

Firstly, let's denote the total number of commuters as C. The commuters who use subway/bus can be represented as 0.70C and those who use taxis/Uber as 0.50C. The number of commuters who use both can be left as the given value, 596,500.

We can express the situation with the following equation:

0.70C + 0.50C - Both = C

Where 'Both' equals 596,500. Simplifying the equation gives:

1.20C - 596,500 = C

Which can then be solved for C:

C = 596,500 / 0.20

C = 2,982,500

Therefore, the total number of commuters in the city is 2,982,500.