Question

6. Pop's Cycle Shop sells bicycles and tricycles. The number of bicycles is 1 less than 5 times the number

of tricycles. All the bicycles and tricycles together have a total of 154 wheels. Find how many bicycles
and tricycles are there.

Answer 1

After solving the system of equations, we found that Pop's Cycle Shop has 12 tricycles and 59 bicycles.

Step-by-step explanation:

The problem at hand is a system of equations word problem which is part of middle school mathematics. We are given two pieces of information about the relationship between bicycles and tricycles at Pop's Cycle Shop:

1. The number of bicycles is one less than five times the number of tricycles.
2. All bicycles and tricycles together have a total of 154 wheels.

Let's denote the number of tricycles as T and the number of bicycles as B. According to the first piece of information, B = 5T - 1. Since a tricycle has 3 wheels and a bicycle has 2 wheels, the second piece of information translates to 3T + 2B = 154 wheels.

Now let's solve this system of equations using substitution or elimination method.

Step 1: Set up the equations

B = 5T - 1 (Equation 1)

3T + 2B = 154 (Equation 2)

Step 2: Substitute Equation 1 into Equation 2

3T + 2(5T - 1) = 154

3T + 10T - 2 = 154

13T - 2 = 154

13T = 156

T = 12

Step 3: Use the value of T to find B

B = 5(12) - 1

• B = 60 - 1
• B = 59

There are 12 tricycles and 59 bicycles at Pop's Cycle Shop.

Answer 2

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Actually Welcome to the Concept of the Linear equations.

Let the number of bicycles = x

and number of tricycles = y

the relationship given is,

x = 5y-1

number of wheels of bicycle = 2x and of tricycles=3y

and other relation is, 2x+3y = 154

so now substituting we get as,

==> 2(5y-1) +3y= 154

10y-2+3y = 154

13y = 154+2

=> y = 12

=> 12*3 = 36 wheels of tricycles

so, 154-36 => 118 wheels of the bicycle.

so the number of bicycles = 118/2 = 59

hence,

==> number of bicycles = 59 and tricycles = 12