How many pounds of nuts selling for$6/lb and raisins selling for $3/ lb should a person combine to obtain150 lb of trail mix selling for $4/lb?
Let x=nuts and y=raisins
two equations:
I.)
x+y=150
3x+6y/150=4
3x+6y=600
II.)
x+y=150
x=150-y
Plug II.) into I.) and solve for y:
3(150-y)+6y=600
450-3y+6y=600
3y=150
y=50
Solve for x using II.)
x+50=150
x=100
To determine the number of pounds of nuts and raisins needed to obtain 150 pounds of trail mix, we can set up a system of equations.
Let's assume x represents the number of pounds of nuts and y represents the number of pounds of raisins.
Equation 1: x + y = 150 (Total weight of the trail mix is 150 pounds)
Equation 2: 6x + 3y = 4 * 150 (Total cost of the trail mix is 150 times the price per pound)
Now, we can solve this system of equations to find the values of x and y.
Multiply Equation 1 by 3 to eliminate y:
3x + 3y = 450
Subtract Equation 2 from the modified Equation 1:
(3x + 3y) - (6x + 3y) = 450 - (4 * 150)
-3x = 450 - 600
-3x = -150
Divide both sides of the equation by -3:
x = -150 / -3
x = 50
Now, substitute the value of x back into Equation 1 to find y:
50 + y = 150
y = 150 - 50
y = 100
So, a person should combine 50 pounds of nuts (selling for $6/lb) and 100 pounds of raisins (selling for $3/lb) to obtain 150 pounds of trail mix (selling for $4/lb).