Acompany sells herb blends for cooking. the tables below show the number of teaspoons of each herb in each blend and the cost for each blend.

number of teaspoons of herb per blend

basil
oregano
parsley
blend 1
1
2
3
blend 2
1
1
2
blend 3
2
2
1

cost
blend 1
$1.06
blend 2
$0.72
blend 3
$0.99

what is the cost of basil per teaspoon?
$0.15
$0.18
$0.19
$0.23

  $0.23

Step-by-step explanation:

You can subtract the cost of Blend 3 from double the cost of Blend 2 and you will find the value of Parsley:

  2(1 tsp Basil + 1 tsp Oregano + 2 tsp Parsley) - (2 tsp Basil + 2 tsp Oregano + 1 tsp Parsley) = 2($0.72) - ($0.99)

  3 tsp Parsley = $0.45 . . . . . simplify

Dividing by 3, we find

  1 tsp Parsley = $0.15

__

Now we can subtract the cost of Blend 1 from double the cost of Blend 2 and subtract another tsp of Parsley to find the cost of Basil.

  2(1 tsp Basil + 1 tsp Oregano + 2 tsp Parsley) - (1 tsp Basil + 2 tsp Oregano + 3 tsp Parsley) - (1 tsp Parsley) = 2($0.72) - ($1.06) - ($0.15)

  1 tsp Basil = $0.23 . . . . . simplify

_____

I find it easier to work systems of linear equations like this using a calculator capable of "row reduction". Each equation of the system corresponds to one row of an "augmented matrix." Input to an on-line calculator is shown in the first attachment; its output is shown in the second attachment. Since the price of Basil is the first variable, its value of 0.23 per tsp is the value the question is asking for.

Basically, reduction of the augmented matrix to row-echelon form is a systematic way to solve the system by elimination. Since we were only looking for the cost of Basil, we didn't have to solve the entire system.

Had we used Cramer's method, we would have arrived at the solution by evaluating the determinants of two 3×3 matrices. The method shown above uses fewer calculations. (It also requires a certain amount of insight or "trial and error" to find an efficient way to get the answer to the question.)

step-by-step explanation: where's the phrase?

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24