Together, a skateboard and a bicycle cost $199.00. The skateboard costs $51.00 less than the bicycle. How much does each cost?

Let

S = cost of skateboard

B = cost of bicycle.

We are given that skateboard and bicycle cost $199.00. We can write this algebraically as

S + B = 199 (Equation 1)

We also know that the skateboard costs $51.00 less than the bicycle. We write this algebraically as

S = B - 51 (Equation 2)

Substituting Equation 2 in Equation 1, we get

S + B = 199

--> (B - 51) + B = 199

--> B - 51 + B = 199

--> 2B - 51 = 199

--> 2B - 51 + 51 = 199 + 51

--> 2B = 250

--> 2B / 2 = 250 / 2

--> B = 125

Now substituting this value B = 125 in Equation 2 gives

S = B - 51 = 125 - 51 = 74

So S = 74 and B = 51 implies that the skateboard costs $74 and the bicycle costs $125.