Question

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

Answer 1

Answer: 12 pounds

Explanation:

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

`\begin {array}l&\underline{Quantity}&\underline{Cost}&\underline{\qquad Qty* 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

Answer 2

12 pounds

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)