I need help with the below question

Question

 a store is having a sell on walnuts and chocolate chips. for three pounds of walnuts and five pounds of chocolate chips the total cost is 21.00. for six pounds of walnuts and two punds of chocolate chips the total cost is 24.00. find the cost of each pound of walnuts and each pound of chocolate chips

Answer 1

Wendy, sometimes it’s harder to translate the problems into math than to do the math.

First, identify the quantities of interest:

Let w be the cost of a pound of Walnuts

Let c be the cost of Chocolate chips

Next translate other information into equations:

total cost of 3 pounds walnuts and 5 pounds chocolate chips is $21.

3w + 5c = 21

6 pounds walnuts plus 2 pounds chocolate chips = 24

6w + 2c = 24

I assume you know how to solve these equations, but here’s the beginning, for those who haven’t.

Double the first equation, this makes the x coefficient equal to that of the second equation

6w + 10c = 42

subtract the second equation

8c = 18

solve

c = 9/4 = $2.25

substitute into first equation

3w + 5*9/4 = 21

put all terms over denominator 4

12w + 45 = 84

solve for w

w = 39 / 12 = $3.25

then cross check

3w + 5c = 21

3*3.25 + 5*2.25 = 21

6w + 2c = 24

6*3.25 + 2*2.25 = 24