You are a manufacturer of a certain item. You’ve calculated that you can sell 80 of these items for $5 each and you can sell 60 of these items for $8 each.
Assuming this relationship is linear, write an equation that relates cost to the number of watches you make
Let p be the price, and N be the sales
If there's a linear relationship,
N = mp + b
Now plug in what you know:
80 = 5m + b
60 = 8m + b
20 = -3m
m = -20/3
b = 340/3
so,
3N = -20p + 340
P=200$Q=85
To find the equation that relates cost to the number of watches manufactured, we need to determine the slope and y-intercept of the linear relationship.
Let's assign the number of watches manufactured as "x" and the cost as "y". We have two data points:
1. Selling 80 watches for $5 each: (80, 5)
2. Selling 60 watches for $8 each: (60, 8)
We can use these data points to calculate the slope (m) of the linear equation using the formula:
m = (y2 - y1) / (x2 - x1)
Using the first data point (80, 5) and the second data point (60, 8):
m = (8 - 5) / (60 - 80)
m = 3 / (-20)
m = -3/20
Now that we have the slope (m), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (80, 5):
y - 5 = (-3/20)(x - 80)
Expanding and simplifying the equation:
y - 5 = (-3/20)x + 12
y = (-3/20)x + 12 + 5
y = (-3/20)x + 17
Therefore, the equation that relates cost (y) to the number of watches manufactured (x) is:
cost = (-3/20)(number of watches) + 17