Write the equation for this situation: the value, v, in hundreds of dollars, of Bob’s stamp collection is 12 dollars more than 1/3 of the age, t (in years).
Then graph the equation and use the graph to determine the value of Debbie’s coin collection if it is 9 years old.
V = (1/3)t + 12.
The equation for Bob's stamp collection can be written as:
v = (1/3)t + 12
To graph this equation, we can plot values of t on the x-axis and corresponding values of v on the y-axis.
Now, let's substitute t = 9 into the equation to find the value of Debbie's coin collection when it is 9 years old:
v = (1/3)(9) + 12
v = 3 + 12
v = 15
Therefore, when Debbie's coin collection is 9 years old, its value would be 15 hundred dollars.
To write the equation for this situation, we need to consider the given information. The value, v, in hundreds of dollars, of Bob's stamp collection is 12 dollars more than 1/3 of the age, t, in years. We can break down the problem step by step to form the equation.
Step 1: Determine 1/3 of the age, t.
We can represent this as t/3.
Step 2: Add 12 dollars more to 1/3 of the age, t.
So, the value, v, can be represented as (t/3 + 12).
Step 3: Convert the value to hundreds of dollars.
Since the value is given in hundreds of dollars, we divide the whole equation by 100:
v = (t/300 + 12/100).
Now, we can use this equation to determine the value of Debbie's coin collection when it is 9 years old.
To graph the equation, we need to plot points on a coordinate plane. In this case, we will use the age, t, on the x-axis and the value, v, on the y-axis, representing the value in hundreds of dollars.
Let's assume a range for the age, t, from 0 to 10 (years).
For t = 0, we substitute it into the equation to find v:
v = (0/3 + 12/100) = 0.12.
For t = 10, we substitute it into the equation to find v:
v = (10/3 + 12/100) ≈ 3.40.
Now, we can plot the points (0, 0.12) and (10, 3.40) on the graph.
Using the graph, we can determine the value of Debbie's coin collection when it is 9 years old. We locate the point where t = 9 on the x-axis and draw a vertical line until it intersects with the graph. Then, we drop a line from this point to the y-axis to find the corresponding value, v. The value (in hundreds of dollars) where the line intersects the y-axis represents the value of Debbie's coin collection when it is 9 years old.