Mathematics, 28.06.2019 13:30 renegade2020

Afarmer plants apple, pear, and cherry trees in an orchard. the number of apple trees is 8 more than twice the number of pear trees. the number of cherry and pear trees combined is 11 more than the number of apple trees. the farmer plants 143 trees total. how many of each type of tree did the farmer plant in the orchard?

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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.

⇒ x = 2y + 8 .....[1]

Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.

⇒ y + z = x + 11 ......[2]

The farmer plants 143 trees total.

⇒ x +y +z =143 .....[3]

Substitute equation [2] into [3] we get;

x + x + 11 = 143

Combine like terms;

2x +11 = 143

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;

66 -8 =2y + 8 -8

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

Answer from: Quest

I’m confused this is what i’m doing in class but the question is confusing

Answer from: Quest

the speed is $135$ miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

$y/x=k$

for the point $(1.5,90)$

substitute the values of x and y

$k=90/1.5=60\ miles/hour$

the linear equation is equal to

$y=60x$

statements

case a) it takes $2$ hours to go $120$ miles

the statement is true

because

substitute

for $x=2$

find the value of y in the linear equation

$y=60(2)=120\ miles$ > is correct

case b) the speed is $135$ miles per hour

the statement is false

because the speed is $60\ miles/hour$

case c) the unit rate for the trip is $60\ miles/hour$

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took $20$ minutes to go the first $20$ miles

the statement is true

because

substitute

for $x=20\ minutes=(1/3)\ hour$

find the value of y in the linear equation

$y=60(1/3)=20\ miles$ > is correct

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Afarmer plants apple, pear, and cherry trees in an orchard. the number of apple trees is 8 more than...

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