Question

A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represent this situation. How many acres of each crop should the farmer plant?

Answer 1

c=number of acres of corn
w=number of acres of wheat

total is 180 acres

c+w=180

wants to plant 3 times as many corn as wheat
c=3w

subsitute 3w for c in other

c+w=180
3w+w=180
4w=180
divide boh sides by 4
w=45

sub back
c=3w
c=3(45)
c=135

135 acres of corn and 45 acres of wheat

Answer 2

The farmer should plant 135 acres and 45 acres 135 acres of corn and wheat respectively.

• Let the acres of corn be C.

• Let the acres of wheat be W.

Given the following data:

• Area of land = 180-acre

To write a system of linear equations that represent this situation:

Translating the word problem into an algebraic expression, we have;

A farmer plants corn and wheat on a 180-acre farm

$C+W = 180$  ......equation 1

Three times as many acres of corn as wheat:

$C = 3W$   ......equation 2.

Substituting eqn 2 into eqn 1, we have:

$3W + W = 180\\\\4W = 180\\\\W = \frac{180}{4}$

W = 45 acres.

For corns:

$C = 3W$  

$C = 3 \times 45$

C = 135 acres.

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