In a shop, There are 25 bicycles and tricycles. There are 63 wheels in all. Find the number of bicycles in the shop.
Let bicycles = x, and tricycles = y
The algebraic equation using the number of wheels and the number of tricycles and bicycles is:
x + y = 25
2x + 3y = 63
I can multiply the top equation by two and subtract from the second one:
2x + 3y = 63
-(2x + 2y = 50)
which gives
y = 13 tricycles
Finally, I substitute y into the equation and I get x = 12 bikes
There are 12 bicycles and 13 tricycles in the shop.
Let's assume the number of bicycles in the shop is x.
The number of tricycles can be found by subtracting the number of bicycles from the total number of bicycles and tricycles:
Number of tricycles = 25 - x
Since each bicycle has 2 wheels and each tricycle has 3 wheels, we can find the total number of wheels by multiplying the number of bicycles by 2 and the number of tricycles by 3:
2x + 3(25 - x) = 63
Now, let's solve this equation step by step:
Step 1: Distribute the 3
2x + 75 - 3x = 63
Step 2: Combine like terms
-1x + 75 = 63
Step 3: Move the constant term to the other side of the equation by subtracting 75 from both sides
-1x = 63 - 75
Step 4: Simplify
-1x = -12
Step 5: Divide both sides by -1 to solve for x
x = -12 / -1 = 12
Therefore, there are 12 bicycles in the shop.
To find the number of bicycles in the shop, we need to set up a system of equations based on the given information.
Let's assume the number of bicycles in the shop is x, and the number of tricycles is y.
Since every bicycle has 2 wheels and every tricycle has 3 wheels, we can set up the following equation:
2x + 3y = 63 (equation 1)
We also know that the total number of bicycles and tricycles is 25, so we can set up another equation:
x + y = 25 (equation 2)
Now, we have a system of two equations with two variables. We can solve these equations to find the number of bicycles in the shop.
To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method:
Multiply equation 2 by 2:
2x + 2y = 50 (equation 3)
Now, subtract equation 3 from equation 1:
(2x + 3y) - (2x + 2y) = 63 - 50
This simplifies to:
y = 13
Substitute the value of y into equation 2:
x + 13 = 25
Subtract 13 from both sides:
x = 25 - 13
x = 12
Therefore, there are 12 bicycles in the shop.
b + t = 25
2 b + 3 t = 63
3 b + 3 t = 75
2 b + 3 t = 63
---------------subtract
1 b + 0 = 12
b = 12