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
