A local grocery store makes a 9-pounds mixture of trail mix. The trail mix contains raisins, sunflower seeds, and chocolate-covered peanuts. The raisins cost $2 per pound, the

sunflower seeds cost $1 per pound, and the chocolate-covered peanuts cost $1.50 per

pound. The mixture calls for twice as many raisins as sunflower seeds. The total cost of the

mixture is $14.50. How much of each ingredient did the store use?

The quantity of each ingredient used:

2 pounds of sunflower, 4 pounds of raisins and 3 pounds of chocolate-covered peanuts.

Step-by-step explanation:

From the question, the total weight of the mixture is 9 pounds.

Also, the mixture calls for twice as many raisins as sunflower seeds, (that is for every 1 pound of sunflower, we have 2 pounds of raisins)

Let the weight of the sunflower seeds be s pounds

Then, the weight of the raisin will be 2s pounds

The weight of chocolate-covered peanuts will be the sum of the weights of the raisin and sunflower seeds deducted from 9 pounds, that is

9 - (2s + s) = 9 - 3s pounds

Hence, the mixture contains 9-3s chocolate-covered peanuts.

Now, from the question, the raisins cost $2 per pound, the  sunflower seeds cost $1 per pound, and the chocolate-covered peanuts cost $1.50 per per pounds; and the total cost of the mixture is $14.50. Then, we can write that

$2(2s) + $1(s) + $1.5(9-3s) = $14.50

$4s + $1s + $13.5 -$4.5s = $14.50

$0.5s = $14.50 - $ 13.50

$0.5s= $1.00

s = $1.00 / $0.5

s = 2

Hence, the weight of sunflower used is 2 pounds

The weight of raisin used is 2s = 2*2 pounds = 4 pounds

and the weight of chocolate-covered peanuts is 9 - 3x = 9 - 3*2 pounds

= 9 - 6 pounds = 3 pounds

Hence, the quantity of each ingredient used:

2 pounds of sunflower, 4 pounds of raisins and 3 pounds of chocolate-covered peanuts.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)