We have a system of three linear equations in three variables
Let x represent each apple, y represent each blueberry , and z represent each cherry.
You have picked up 24 pounds of there different types of fruit at a farm. The linear equation which represents this is x+y+z =24 \rightarrow equation 1.
Twice the many pound of apples as the other two fruits combined can be represented by the linear equation
x = 2(y+z)\rightarrow equation 2.
The apples cost $1.40 per pound, blueberries cost $0.90 per pound, cherries cost $1.10 per pound which costs $30. The linear equation which represents this will be
1.40 x + 0.9 y + 1.1 z = 30\rightarrowequation 3.
Now we solve this by good old elimination and substitution method.
Solving equation 1 and 2,
x+ y + z = 24
x -2y-2z = 0
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2x+2y+2z = 48 (multiplying equation 1 by 2)
x-2y-2z = 0
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3x = 48
\Rightarrow x = 16
Now plug in this value of x in equation 1 to get y+z = 24 - 16 = 8
and equation 3 to get 1.4 \times 16 + 0.9 y + 1.1 z = 30 or 0.9 y + 1.1 z = 30 - 22.4 = 7.6
Multiplying y+z = 8 with 0.9 we get
0.9y + 0.9 z = 7.2
\mp 0.9 y \mp 1.1 z = \mp 7.6
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-0.2 z = -0.4
z = 2
Plugging the values of x and z in equation 1, we get y = 24 - 16 - 2 = 24 - 18 = 6
So, the number of apples are 16, the number of blueberries are 6, and the number of cherries are 2.