I have beans that sell for $9 per pound and $12 per pound, they need to be mixed to create 100lbs of mixture that will sell for $11.25 per pound . How much of each type of bean should be used in the mixture?
X=#lbs beans that sell for $9.00/lb.
Y=#lbs beans that see for $12.00/lb.
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X+Y=100 eqn 1 equates to total lbs.
9X + 12Y = 100*11.25=1125 eqn 2 is cost.
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Two equations. Two unknowns. Solve simultaneously.
Post your work if you get stuck.
To solve this system of equations, we can use the method of substitution or elimination. Since equation 1 is already solved for X, we can substitute this value into equation 2 and solve for Y.
From equation 1:
X + Y = 100
Substitute X = 100 - Y into equation 2:
9(100 - Y) + 12Y = 1125
Distribute the 9:
900 - 9Y + 12Y = 1125
Combine like terms:
3Y = 225
Divide both sides by 3:
Y = 75
Now, substitute this value of Y back into equation 1 to solve for X:
X + 75 = 100
Subtract 75 from both sides:
X = 25
Therefore, to create a 100-pound mixture that sells for $11.25 per pound, you should use 25 pounds of beans that sell for $9 per pound and 75 pounds of beans that sell for $12 per pound.