Question

I need help setting up this problem. Please help me out.

Answer 1

Answer:

  12 pounds

Step-by-step explanation:

One quantity is asked for, so it is convenient to let a variable represent that. We can use x to represent pounds of chocolate. Then the total cost of the mix is ...

  19.30·x + 3.50·18 = 9.82·(x +18) . . . . cost of chocolate + cost of trail mix

  9.48·x = 113.76 . . . . . . simplify, subtract 63+9.82x

  113.76/9.48 = x = 12 . . . . . . divide by the coefficient of x

The owner needs to mix 12 pounds of chocolate. (no rounding necessary)

Answer 2

Answer:  12 pounds

Step-by-step explanation:

Use Quantity x Cost. Create a table (multiply across and add down)

$\begin {array}{l|c|c||l}&\underline{Quantity}&\underline{Cost}&\underline{\qquad Qty\times Cost\qquad }\\Chocolate&x&19.30&x(19.30)=19.30x\\\underline{Trail\ Mix}&\underline{\qquad 18\qquad }&\underline{\ 3.50\ }&\underline{\ 18(3.50)=63\qquad }\\Mixture&x+18&9.82&19.30x+63\\\end{array} \\\\\\\text{The Mixture line creates the equation:}$

  (x + 18)(9.82) = 19.30x + 63

9.82x + 176.76 = 19.30x + 63          distributed 9.82 into x+18

             176.76 = 9.48x + 63         subtracted 9.82x from both sides

             113.76 = 9.48x                 subtracted 63 from both sides

                   12 = x                     divided both sides by 9.48