A spring is 3 in. long with no weight suspended from it. For each ounce of weight, the spring stretches 0.2 in. Unitl it reaches its maximum lenght of 9 in. How much weight must be added for the spring to reach its maximum length? algebra
Whats the variable and equation
Let's assume the variable x represents the weight that needs to be added to the spring.
The equation that represents the relationship between the weight added and the elongation of the spring is:
0.2x = 9 - 3
In this equation, 0.2x represents the elongation of the spring due to the weight added (0.2 inches per ounce), while 9 - 3 represents the elongation of the spring when no weight is added (9 inches - 3 inches = 6 inches).
To find the weight that must be added for the spring to reach its maximum length, we need to solve this equation for x:
0.2x = 6
Dividing both sides of the equation by 0.2, we get:
x = 6 / 0.2 = 30
Therefore, 30 ounces of weight must be added for the spring to reach its maximum length.