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.
