Question

When planning his crops, Farmer Tim knows that his 7 acres can support peas and carrots. He wants to make $7,000 from his crops. He can make $2,000 per acre of peas (the variable p) and $1,000 per acre of carrots (the variable c). Which equation below would be a constraint in his system of equations?

a. 2,000p + 1,000c = 7,000
b. 2,000p − 1,000c = 7,000
c. p + c = 7
d. c − p = 7

Answer 1

The correct option is C). p + c = 7

Explanation:

Let number of acres available for peas = p acre

And number of acres available for carrot = c acre

Now, One acre of peas make $2000

And one acre of carrot makes $1000

So, to make a total amount of $7000, the required equation is :

2000p + 1000c = 7000

and total available acres of land for planning the crops = 7 acres

⇒ p + c = 7

Hence, the equation of the problem is : 2000p + 1000c = 7000 with subject to the constraints : p + c = 7

Therefore, The correct option is C). p + c = 7

Answer 2

This is the concept of algebra, we are required to get the equation that would be a constraint in the system of equation,
The total amount that the farmer want to make is $7000
amount he can make per acre of land is $2000, the amount he can make per acre will $1000. The variable representing peas and carrots are p and c retrospectively;
The total amount made from this can be represented by the equation below;
Total amount made by p acres of peas will be:
2000*p=$ 2000p
Total amount made by c acres of carrots:
1000*c=$1000c
Total amount will be given by:
2000p+1000c=7000

this can be simplified by dividing through by 1000 to get:
p+c=7

The correct answer is C.