Respuesta :
Answer:
Let x represents the number of apple tree and y represents the number of pear tree and z represents the number of cherry tree in an orchard.
From the given statement: The number of apple trees is 8 more than twice the number of pear trees.
⇒ [tex]x = 2y + 8[/tex] .....[1]
Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.
⇒[tex]y + z = x + 11[/tex] ......[2]
The farmer plants 143 trees total.
⇒[tex]x +y +z =143[/tex] .....[3]
Substitute equation [2] into [3] we get;
[tex]x + x + 11 = 143[/tex]
Combine like terms;
[tex]2x +11 = 143[/tex]
Subtract 11 on both sides we get;
2x + 11 -11 =143 -11
Simplify:
2x = 132
Divide both sides by 2 we get;
x = 66
Substitute the value of x in equation [1];
66 = 2y + 8
Subtract 8 on both sides we get;
[tex]66 -8 =2y + 8 -8[/tex]
Simplify:
58 = 2y
Divide by 2 on both sides we get;
y = 29
Substitute the value of x and y in equation [3];
we have;
29 + 66 + z = 143
95 + z =143
Subtract 95 on both sides, we get;
95+ z -95 = 143- 95
Simplify:
z = 48
The framer plant in the orchard = 66 apple trees , 29 pear trees and 48 cherry trees
