The owner of a bike shop sells tricycles (3 wheels) and bicycles (2 wheels), keeping inventory by counting seats and wheels. one day she counts 40 seats and 95 wheels. how many of each type of cycle are there?

25 bicycles and 15 tricycles

Step-by-step explanation:

The owner of a bike shop sells tricycles ( 3 wheels ) and bicycles (2 wheels).

In her inventory she counts the number of seats = 40

and number of wheels = 95

Let the number of bicycle are x and tricycles are y,

Then as per statement "One day she counts 40 seats"

equation will be x + y = 40 (1)

Now as per second statement "she counts 95 wheels"

Equation will be 2x + 3y = 95 (2)

We multiply equation (1) by 2 and subtract it by equation (2).

2x + 3y - 2(x+y) = 95 - 80

2x + 3y - 2x - 2y = 15

y = 15

Now to calculate the value of x will put y = 15 in equation (1)

x + 15 = 40

x = 40 -15

x = 25

There are 25 bicycles and 15 tricycles

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.