For each situation first write and equation in the form of y=mx + b. Then solve each problem.
A farm has 75 acres of wheat. The farmer can harvest the wheat from 12 acres per day. In how many days will all of the fields be harvested?
y=12x + 75
74/12=6.25
substitute x for 6.25
12 x 6.25=75
75 + 75=150
Is 150 the answer?
Would it actually be 6.25 days to harvest the field or rounded to 7 days?
Is the equation correct?
y=12x+75
or would it be
75=12x + b?
what does y represent? x?
If y represents the amount of wheat yet to be harvested after x days, then
y = 75-12x
or,
y = -12x+75
Try to see what your equations would represent ...
Now you want to find x when all the wheat has been harvested -- that is, when y=0
And yes, x=6.25
x is the value where the line intercepts the x axis and I am not sure what y represents?
Hello Steve,
You put y = -12x+75
If do -12 x 6.25=75
-75 + 75=0
Hello Steve,
I think I know why you put the below.
If y represents the amount of wheat yet to be harvested after x days, then
y = 75-12x
or,
y = -12x+75
both answers would equal 0 for y am I correct?
correct. After 6.25 days there is no wheat left to be harvested.
Before you can write a meaningful equation, you need to decide what the variables mean. Without that, you're just guessing. You could come up with a different equation, but make sure that it means what you intend, and solving it answers the question asked.
So would the correct answer be:
y= -12x + 75 in order to write it as y=mx + b?
dont agree
To solve the problem, we start by writing an equation in the form of y = mx + b, where y represents the total acres of wheat harvested, x represents the number of days, m represents the rate of harvesting per day, and b represents the initial amount of wheat.
In this situation, we know that the farmer can harvest 12 acres of wheat per day and initially has 75 acres of wheat. Therefore, we can write the equation as:
y = 12x + 75
To find the number of days it will take to harvest all the fields, we need to solve for x. We can do this by setting y equal to the total amount of wheat, which in this case is 75 acres.
75 = 12x + 75
Next, we can solve for x by subtracting 75 from both sides of the equation:
0 = 12x
Dividing both sides of the equation by 12, we get:
0/12 = x
x = 0
However, this solution x = 0 does not make sense in this context since it means that it takes zero days to harvest all the fields, which is not possible.
The mistake in your calculation might be that you substituted x for 6.25, but it should be the other way around. When we substitute x = 6.25 into the equation y = 12x + 75, we can calculate the value of y:
y = 12(6.25) + 75
y = 75 + 75
y = 150
Therefore, it will take 6.25 or approximately 6 days to harvest all of the fields. So the correct answer is 6 days, not 150.