Name
PreAlg
Systems by Graphing. Word Problems: Homework 1
For each problem, write a system of equations, graph both lines, and then use the intersection point
to answer the question(s).
1. Scientists studied the weights of two alligators over a period of 12 months. The initial weight
and growth rate of each alligator are shown below.
Alligator 1
Initial Weight: 4 pounds
Rate of Growth: 1.5 pounds per month
Alligator 2
Initial Weight: 6 pounds
Rate of Growth: 1 pound per month
After how many months did the alligators weigh the same amount?
Let
= the weight of the alligator
Let
= time in months
Equation for Alligator 1:
Time
Weight
0
1
2
3
After
Equation for Alligator 2:
Time
Weight
0
1
2
3
months, both alligators weighed
pounds.
2. Tickets for a concert cost $10 each if you order them online plus a service charge of $8 per
order. The tickets are $12 each if you buy them at the door the night of the concert. For how
many tickets will the cost be the same whether you buy the tickets online or at the door the
night of the concert?
Let
Let
= number of tickets bought
= total cost of tickets
Equation for Online Purchase:
Number of Tickets
0
1
2
3
Total Cost
The cost is the same whether you buy
the door.
Equation for Night of the Concert Purchase:
Number of Tickets
0
1
2
3
tickets for a cost of
Total Cost
online or at
3. Manny’s Music Rental charges a fee of $40 plus $25 per month to rent a saxophone. Sid’s
Saxophones charges $25 plus $30 per month to rent the same saxophone.
Write a system of equations to represent the situation.
Let
= number of months
Let
= the total cost
Manny’s Music Rental:
Number of Months
0
2
4
6
Sid’s Saxophones:
Total Cost
Number of Months
0
2
4
6
What conclusion can you reach from the graph?
Total Cost