# A 5-lb nut mixture is worth $2.80 per pound. The mixture contains peanuts worth$1.70 per pound and cashews worth $4.55 per pound. How many pounds of each type of nut are int he mixture? ##### 2 Answers Jun 4, 2015 Let's call the amount of cashew nuts $x$Then the amount of peanuts is $5 - x$because we have 5 lbs in total. 5 lbs of mixture is 2.80*5=$14.00

This is equal to $1.70*(5-x)+$4.55*x=$14.00 Now work away the brackets first, keep all the $x$'s on the left, and put the dollars to the right, divide, and you'll find $x$, the amount of cashew nuts. The rest is peanuts :-) Jun 4, 2015 Let $x \in \left[0 , 1\right]$be the weight of cashews in one pound of mixture. Then one pound of mixture contains $\left(1 - x\right)$pounds of peanuts. Equating the costs in dollars, we have: $2.80 = 1.70 \left(1 - x\right) + 4.55 x$$= 1.70 - 1.70 x + 4.55 x$$= 1.70 + 2.85 x$Subtract $1.70$from both ends to get: $2.85 x = 1.10$So $x = \frac{1.10}{2.85} = \frac{110}{285} = \frac{22}{57}$pounds of cashews per pound of mixture and $1 - x = 1 - \frac{22}{57} = \frac{35}{57}$pounds of peanuts per pound of mixture In 5-lb of mixture there is $5 \cdot \frac{22}{57} \cong 1.93$lb of cashews and $5 \cdot \frac{35}{57} \cong 3.07\$ lb of peanuts.