Question

You are buying vehicles (tricycles and unicycles). Each tricycle and unicycle has two pedals. A unicycle only has one wheel whereas a tricycle has three wheels. What is the difference between the number of tricycles and unicycles if there is a total of 337 wheels and 330 pedals?

*Please give steps on how to solve it

Answer 1

So for this you are going to be using a system of equations. The first equation is gonna equal the # of wheels and the second equation is gonna equal the # of pedals.

Let x equal # of tricycles and y equal # of unicycles.

The first equation is gonna be
`3x+y=337`

The second equation is gonna be
`2x+2y=330`

For this, I'll be using the substitution method. And to be able to do that, you'll be subtracting 3x on each side of the first equation to get
`y=-3x+337` .

And with this, you are going to substitute y in the second equation for (-3x+337) since that is the equivalent to y according to the first equation; and your second equation should look like this:
`2x+2(-3x+337)=330` . From here we can solve for x.

First multiply 2 with (-3x+337), and your equation should look like
`2x-6x+674=330`

Combine like terms to get
`-4x+674=330`

Subtract 674 on each side to get
`-4x=-344`

And then divide -4 on each side, and your answer should be
`x=86`



Now that we know that x is 86, we can replace x for 86 in either equation to solve for y. For this, i'll be substituting in the first equation.


`3(86)+y=337`

Multiply 86 with 3 to get
`258+y=337`

And then just subtract 258 on each side to get
`y=79`


So since we now know that there are 86 tricycles and 79 unicycles, we just need to subtract them to get the final answer.


`86-79=7`

There are 7 more tricycles than unicycles.