Question

Some one answer ASAP!! in trail mix, there are nuts and dried fruit. In one mix there is 40% dried fruit. In another, there is 60% dried fruit. How many pounds of each mix is needed to make 5 pound mix that is 55% dried fruit?

let x= The amount of 40% fruit mix
let y=the amount of 60% fruit mix

what is the solution to the system

Answer 1

`p\%=(p)/(100)\\\\40\%=(40)/(100)=(4)/(10)=0.4;\ 60\%=(60)/(100)=(6)/(10)=0.6;\ 55\%=(55)/(100)=0.55\\\\\left\{\begin{array}{ccc}x+y=5&\to x=5-y\\0.4x+0.6y=0.55\cdot5\end{array}\right\\\\\text{Use substitution method}\\\\0.4(5-y)+0.6y=2.75\qquad\text{use distributive property}\\\\(0.4)(5)+(0.4)(-y)+0.6y=2.75\\\\2-0.4y+0.6y=2.75\qquad\text{subtract 2 from both sides}\\\\0.2y=0.75\qquad\text{multiply both sides by 5}\\\\\boxed{y=3.75}`

`\text{Put the value of y to the first equation}\\\\x=5-3.75\\\\\boxed{x=1.25}\\\\Answer:\ x=1.25\ and\ y=3.75.`