The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?
1 answer:
Answer:
The value of x is -3
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope of a line that passes through points (x1 , y1) and (x2 , y2) is
* Lets solve the problem
∵ The points (4 , 1) and (x , -6) lie on the same line
∵ The slope of the line is 1
- Let the point (4 , 1) is (x1 , y1) and the point (x , -6) ix (x2 , y2)
∵ x1 = 4 , x2 = x and y1 = 1 , y2 = -6
∴
∴
∵ The slope of the line is m = 1
∴
- By using cross multiplication
∴ x - 4 = -7 ⇒ add 4 to both sides
∴ x = -3
* The value of x is -3
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The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.
Given:
- Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a pound
- The resulting mixture should be 50 pounds of candy
- The resulting mixture should cost $1.30 a pound
To find: The amount of candy costing $1.25 a pound that should be mixed
Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.
Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with '' pounds of candy costing $1.45 a pound.
Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and '' pounds of candy costing $1.45 a pound.
Accordingly, the total cost of the resulting mixture is
However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is
Equating the total cost of the resulting mixture obtained in two ways, we get,
This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.
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