Question

systems of equations
the weight of two alligators was studied over a period of 12 months. alligator 1 had an initial weight of 4 lbs. and rate growth of 2 lbs. per month. alligator 2 had an initial weight of 8 lbs. and a growth rate of 1 lb. per month. after how many months will the alligators weigh the same amount? what is their weight?
equations
alligator 1: ( y = 2x + 4 )
alligator 2: ( y = x + 8 )
method 1: table of values
alligator 1
x | y
0 | 4
1 | 6
2 | 8
3 | 10
4 | 12
5 | 14
alligator 2
x | y
0 | 8
1 | 9
2 | 10
3 | 11
4 | 12
5 | 13
method 2:
graphs for alligator 1, alligator 2, and alligator 1 & alligator 2 are present

Explanation:

Step1: Set up the equations

We have two equations for the weight of the alligators over time \( x \) (in months) and weight \( y \) (in lbs):

• Alligator 1: \( y = 2x + 4 \)
• Alligator 2: \( y = x + 8 \)

Step2: Solve the system of equations

To find when their weights are equal, we set the two equations equal to each other:
\( 2x + 4 = x + 8 \)

Subtract \( x \) from both sides:
\( 2x - x + 4 = x - x + 8 \)
\( x + 4 = 8 \)

Subtract 4 from both sides:
\( x + 4 - 4 = 8 - 4 \)
\( x = 4 \)

Step3: Find the weight

Now we substitute \( x = 4 \) back into one of the equations (let's use Alligator 2's equation \( y = x + 8 \)):
\( y = 4 + 8 \)
\( y = 12 \)

Answer:

After 4 months, the alligators will weigh the same amount, and their weight will be 12 lbs.