A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 12 pounds of chocolate chips, the total cost is $33. For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $15. What is the total cost for each pound of walnuts and each pound of chocolate chips? Hey A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 12 pounds of chocolate chips, the total cost is $33. For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $15. What is the total cost for each pound of walnuts and each pound of chocolate chips?

The total cost of pound of walnut and a pound of chocolate together is $4

Step-by-step explanation:

Let us assume the cost of walnut as $w per pound

Similarly, let us assume the cost of chocolate at $c per pound

Putting the above assumptions in the given conditions mentioned in the question-

Condition 1- the cost of 2-pound walnut and 12-pound chocolate is $ 33

The 2-pound walnut cost can be written as 2w (since we have assumed that walnut cost $w/pound)

Similarly, 12-pound chocolate would cost 12c

2w+12c=33  Equation 1

Condition 2- the cost of 5-pound walnut and 3-pound chocolate is $15

5-pound walnut cost 5w and 3-pound chocolate cost 3c which equals $15

5w+3c=15   Equation 2

Comparing Equation 1 and Equation 2

We multiply Equation 2 with a factor of 4  

Hence the equation 2 becomes- 20w+12c=60 (this was done to make either of the variable’s coefficient equal)

Now subtracting Equation 1 from Equation 2

20w+12c=60 -(2w+ 12c=33)

We get 20w-2w=60-33 (12c gets cancelled out)

18w=27

w=$ 1.5  (cost of walnut is $1.5/pound)

putting the value of w in either of the equation we get c as 2.5$

Hence the total cost of one pound each of walnut and chocolate is $2.5+$1.5= $4

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.