I bought $23.40 worth of two types of bird seed. Thistle bird seeds sells for $1.60 per pound and wild bird seed sells for $0.95 per pound. If she bought 12 pounds of wild bird seed, write and solve a linear equation to find the amount of thistle bird seed she purchased.
Jeff is keeping track of his weight over several weeks.After 2 weeks he weighs 194 pounds . after 6 weeks he weights 186 pounds. write and solve a linear equation to find jeffs weight after 12 weeks.
Let x be the amount of thistle bird seed purchased.
The cost of thistle bird seed is 1.6x dollars.
The cost of wild bird seed is 12 * 0.95 = 11.4 dollars.
The total cost is 1.6x + 11.4 dollars.
Since the total cost is 23.40 dollars, we have the equation:
1.6x + 11.4 = 23.40
Subtracting 11.4 from both sides, we get:
1.6x = 12.00
Dividing both sides by 1.6, we get:
x = 7.5
Therefore, the person purchased 7.5 pounds of thistle bird seeds.
For the second problem:
Let's set up a linear equation using the two given data points.
After 2 weeks: 2 weeks = 194 pounds
After 6 weeks: 6 weeks = 186 pounds
We can find the slope of the line using the two points: (2, 194) and (6, 186).
Slope = (Change in y) / (Change in x) = (186 - 194) / (6 - 2) = -8 / 4 = -2
Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the point (2, 194) and the slope -2, we have:
y - 194 = -2(x - 2)
Simplifying the equation, we get:
y - 194 = -2x + 4
y = -2x + 198
To find Jeff's weight after 12 weeks, we substitute x = 12 into the equation:
y = -2(12) + 198
y = -24 + 198
y = 174
Therefore, Jeff's weight after 12 weeks would be 174 pounds.