Answer:
423
Step-by-step explanation:
Start by setting up a formula.
x = the shorter piece
total = 1313
longer piece = (x*2) + 44
x + (x*2) + 44 = 1313
Simplify
3x + 44 = 1313
Now we must solve for x.
Whatever you do on the left side of the equal sign must also be done on the right.
The goal is to get x by itself on the left side.
Do the easiest thing first, which is usually addition or subtraction. In this case, subtract 44 from both sides.
3x + 44 - 44 = 1313 - 44
3x = 1269
Now the only way to cancel out the 3 on the left is to divide by 3. Since 3/3 =1. Remember this must be done on both sides to keep things equal.
3x/3 = 1269/3
x=423
The End
we will proceed to resolve each case to determine the solution
we have
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
<u>case a)</u> 
Substitute the value of x and y in the inequality
-------> is true
so
The ordered pair is a solution
<u>case b)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case c)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case d)</u> 
Substitute the value of x and y in the inequality
-------> is True
so
The ordered pair is a solution
<u>case e)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
Verify
using a graphing tool
see the attached figure
the solution is the shaded area below the line
The points A and D lies on the shaded area, therefore the ordered pairs A and D are solution of the inequality
X = mary's shells
g = 1 1/4x + 5
n = 1 1/2x+ 1
g = n
1 1/4x + 5 = 1 1/2x + 1
5/4x + 5 = 3/2x + 1...multiply by common denominator of 4, this will get rid of fractions...however, this is optional...u can work with fractions if u wish.
5x + 20 = 6x + 4
5x - 6x = 4 - 20
-x = - 16
x = 16....so Mary has 16 shells
The pricing of the boxes seems to be consistently 2.40 per box. Ethan's cost is
.. 52.80 = 2.40 * (# of boxes)
.. 52.80/2.40 = (# of boxes)
.. 22 = # of boxes
Ethan has bought 22 boxes for 52.80.
3=4m+ b
-1=3m+b
m=4
plug in to either equation,
3=16+ b
b=-13
Thus, C would be the answer.
