After mixing two types of candies, the price became $3.40 per lb. The quantity of the first type of candy was 5/12 of the quantity of the second type. If the price of the first type of candy is $4.60 per lb, what is the price per pound of the second type of the candy?
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Answer:
This is a systems of equations problem where you are given enough information to set up two equations for two variables.
Let x=the amount (lbs) of the first trail mix that costs $2.45/lb.
Let y=the amount (lbs) of the second trail mix that costs $2.30/lb.
You want to find x and y given that:
x + y = 30 lbs (total amount of mixed trail mix)
and that
2.45x + 2.45x+2.30y = $2.35 (30) the cost of each trail mix type added together to equal the final cost
2.45x + 2.3y = 70.5
You now have two equations in terms of x and y that can be solved using substitution or elimination. Let's try substitution.
x + y = 30
2.45x + 2.3y = 70.5
You can easily subtract x from both sides of the first equation, and get y = 30 - x. Substitute this equation into the second equation in place of y
2.45x + 2.3 (30 - x) = 70.5 or (using the distributive property) 2.45x + 2.3(30) - 2.3x = 70.5
Group like terms by rearranging and subtracting 2.3(30) = 69 from both sides of the equation
2.45x - 2.3x + 69 = 70.5
-69 -69
2.45x - 2.3x = 1.5
0.15x = 1.5, now divide each side of the equation by 0.15 and get x alone and then solve for x
0.15 x/ 0.15 = 1.5/0.15
x = 10
use x + y = 30 and substitute in 10 for x, then 10 + y = 30, subtract 10 from each side and solve for y. y = 20.