GIven:
The cost of first type of candy is, c1 = $1.15 per pound.
The cost of second type of candy is, c2 = $2.20 per pound.
The cost per pound of mixed candy is, c = $1.40 per pound.
The total weight of mixed candy is, W = 29 pounds.
The objective is to find the number of pounds of first candy and number of pounds of second candy mixed together.
Explanation:
Consider the number of first type of candy as x and the number of second type of candy as y.
The equation for total pounds of mixed candy can be written as,
[tex]\begin{gathered} x+y=29 \\ x=29-y\text{ . . . . . . (1)} \end{gathered}[/tex]
Since, the cost per pound of mixed candy is $1.40, the total cost of 29 pounds of candy will be,
[tex]\begin{gathered} T=W\times c \\ =29\times1.40 \\ =40.6\text{ dollars} \end{gathered}[/tex]
Then, the equation of total cost can be written as,
[tex]1.15x+\text{2}.20y=40.6\text{ . . . . . . (2)}[/tex]
To find x and y:
Substitute the value of x in equation (2),
[tex]\begin{gathered} 1.15(29-y)+2.20y=40.6 \\ 33.35-1.15y+2.20y=40.6 \\ 1.05y=40.6-33.35 \\ 1.05y=7.25 \\ y=\frac{7.25}{1.05} \\ y\approx7 \end{gathered}[/tex]
Substitute the value of y in equation (1).
[tex]\begin{gathered} x=29-7 \\ x=22 \end{gathered}[/tex]
Hence,
The number of pounds of candy sell for $1.15 is 22.
The number of pounds of candy sell for $2.20 is 7.
