Question

While conducting an inventory in their bicycle shop, the owner noticed the number of bicycles is 2 fewer than 10 times the number of tricycles. They also know there are 410 wheels on all the bicycles and tricycles in the store. Write and solve a system of equations to find the number of bicycles in the store.

Answer 1

Answer:
The number of bicycles in the store is 178\ bicycles178 bicycles
Explanation:
Let
x------> the number of bicycles
y-----> the number of tricycles
we know that
The bicycles has two wheels and the tricycles has three wheels
so
2x+3y=4102x+3y=410 ------> equation A
x=10y-2x=10y−2 ------> equation B
substitute equation B in equation A and solve for y
2(10y-2)+3y=4102(10y−2)+3y=410
20y-4+3y=41020y−4+3y=410
23y=41423y=414
y=18\ tricyclesy=18 tricycles
Find the value of x
x=10(18)-2=178\ bicyclesx=10(18)−2=178 bicycles

Answer 2

The number of bicycles in the store is
`178\ bicycles`

Explanation:

Let

x------> the number of bicycles

y-----> the number of tricycles

we know that

The bicycles has two wheels and the tricycles has three wheels

so

`2x+3y=410` ------> equation A

`x=10y-2` ------> equation B

substitute equation B in equation A and solve for y

`2(10y-2)+3y=410`

`20y-4+3y=410`

`23y=414`

`y=18\ tricycles`

Find the value of x

`x=10(18)-2=178\ bicycles`