5. trail snax corp. mixes raisins that cost $5 per kg with peanuts that cost $3.80 a kg. how many kilograms…

5. trail snax corp. mixes raisins that cost $5 per kg with peanuts that cost $3.80 a kg. how many kilograms of raisins should be mixed with 10 kg of peanuts to obtain a mixture worth $4 per kg?\n6. a card company mixes two varieties of cards. embossed cards cost $0.65 each and regular cards $0.40 each. how many cards of each type should be included in an assortment of 250 cards that cost $142?
Answer
Explanation:
Step1: Set up the cost - equation
Let $x$ be the number of kilograms of raisins. The cost of the raisins is $5x$ dollars, the cost of the 10 kg of peanuts is $3.8\times10 = 38$ dollars, and the total weight of the mixture is $(x + 10)$ kg with a cost of $4(x + 10)$ dollars. So the equation is $5x+38=4(x + 10)$.
Step2: Expand the right - hand side
Expand $4(x + 10)$ to get $4x+40$. So the equation becomes $5x + 38=4x+40$.
Step3: Solve for $x$
Subtract $4x$ from both sides of the equation: $5x-4x+38=4x-4x + 40$. This simplifies to $x+38 = 40$. Then subtract 38 from both sides: $x=40 - 38$.
Answer:
$2$