Answer:
Look for where both functions have the same y value. For example, when x = 3 in #7, both are 5. So the solution is (3,5).
Step-by-step explanation:
Each table has two functions. This forms a system of equations. A system of equations is essentially two conditions that must both be met to produce a solution. A solution can be found as where the two equations are equal. In the table, look for where both functions have the same y value for some x. This will be where the values are the same in the same row. This is the solution and is written as an (x,y) point.
7. When x = 3 both functions are 5. The solution is (3,5).
Area of a rectangle = length times width
So, 3/4*1/4= 3/16 yards^2
The answer is 200 pounds
Let x be the number of pounds of the second chocolate that should be added
First chocolate: 300 pounds
cocoa to caramel = 1 to 7
So, there are in total 8 parts (1 + 7 = 8)
There is:
Cocoa: 1/8 * 300 pounds
Caramel: 7/8 * 300 pounds
Second chocolate: x pounds
cocoa to caramel = 1 to 15
So, there are in total 16 parts (1 + 15 = 16)
There is:
Cocoa: 1/16 * x pounds
Caramel: 15/16 * x pounds
Resulting chocolate: 300 + x pounds
cocoa to caramel = 1 to 9
So, there are in total 10 parts (1 + 9 = 10)
There is:
Cocoa: 1/10 * (300 + x) pounds
Caramel: 9/10 * (300 + x) pounds
Since in all chocolate, there is only one part of cocoa, it is easy to add up the amounts of cocoa:
1/8 * 300 + 1/16 * x = 1/10 * (300 + x)
300/8 + x/16 = 300/10 + x/10
75/2 + x/16 = 30 + x/10
75/2 - 30 = x/10 - x/16
75/2 - 60/2 = 8x/80 - 5x/80
(75 - 60)/2 = (8x - 5x)/80
15/2 = 3x/80
80 * 15/2 = 3x
40 * 15 = 3x
600 = 3x
x = 600/3
x = 200 pounds
3 1/4 = 13/4
1 2/4 = 6/4
So 13/4 - 6/4 = 7/4
7/4 = 1 3/4