Question

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?

Answer 1

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

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