3. Levinson’s Hardware store has a number of bikes and trikes for sale. There are 27 seats and 60 wheels, all told. Determine how many bikes and how many trikes there are?

Question

YOU CAN NOT USE SYSTEM OF EQUATIONS TO SOLVE THIS PROBLEM!

Answer 1

Hello! Actually, you can and should use a system of equations here. You will write out two equations here:

B+T=27

2B+3T=60

where B=number of bikes, T=number of trikes

When you solve this system of equations, you will find that B=21 and T=6.

Detailed Explanation:

You know that there are a total of 27 seats. You also know that each bike has one seat, and each trike also has one seat. So to represent the total number of seats, you need the first equation, B+T=27.

You also know that there are a total of 60 wheels. You also know that a bike has two wheels, and a trike has three wheels. So to represent the number of wheels, you need the second equation 2B+3T=60.

Solve using a system of equations by writing both equations with one on top of the other.

B+T=27

2B+3T=60

Eliminate one of the variables by making the coefficients the same in both equations. Let's eliminate T by multiplying the top equation by 3. NOTE: You have to multiply the entire equation by 3, not just the variable you want to eliminate.

3B+3T=81 (every term in this top equation has been multiplied by 3)

2B+3T=60 (no changes have been made to this equation)

Now subtract the bottom equation from the top equation to eliminate the T variable and to solve for a numerical value of B.

3B-2B=B. 3T-3T =0. 81-60=21.

This will leave you with B+0=21, thus B=21.

Since now you know that B=21, you can plug that number into either equation, to solve for T. I will show how this works using either one.

21+T=27 (this is the top equation). T=27-21=6.

2(21)+3T=60 (this is the bottom equation). 3T=60-2(21)=18. T=18/3=6.

Notice how by plugging B=21 into either equation, you get T=6.

So now you've found your answer, but you're not done yet. You always want to make sure you did the math correctly, so you need to check your work. You can do this by thinking logically through the problem, without using formulas. If you have 21 bikes and 6 trikes, would you have a total of 27 seats? Yes, you would, because you know that both bikes and trikes only have one seat each. Now, if you have 21 bikes and 6 trikes, would you have a total of 60 wheels? Well, if 21 bikes have two wheels each, you'd have 42 wheels from bikes, and if 6 trikes have three wheels each, you would have 18 wheels from trikes. 42 plus 18 is 60, so yes, you would.