Thinking of this Mathematically, we are given a function. The solution to a function is it’s ordered pairs (x, y) that satisfy the equation. Recall that the x-coordinates are your input values (also called domain), and the y-coordinates are your output values (also called range). Essentially, the ordered pair means for that x input, y output is equated. Therefore, we are given the ordered pair (x, 479), since x is unknown and 479 is the total value (f(s)=479). So, plug the given values into the function and solve for “s.”
(479)=13(s-65)+50
• First, apply the distributive property, which states that a(b+c)=ab+ac:
(479)=13s-845+50
Now, combine like terms:
(479)=13s-795
• Use inverse operations to cancel out the -795 and combine it with the alike term of 479:
1,274=13s
• Divide both sides by 13 to cancel out 13•s:
98=s
• Apply the symmetric property:
98=s=98, meaning that s=98 is equal to 98=s.
• Lastly, plug the ordered pair (98, 479) back into the function to check that 98 does indeed satisfy the equation, equaling 479:
F(98)=13((98)-65)+50
• Use PEMDAS to solve:
F(98)=13(33)+50
F(98)=429+50
F(98)=479.
Therefore, the speed was 98mph.