Algebra 1
Name___________________________________________
CW#16 (HW?) Solving Systems of Equations in Word Problems
1. Cost Problems
a) You purchase 8 gallons of paint and 3 brushes for
$152.50. The next day you purchase 6 gallons of
paint and 2 brushes for $113.00. How much does a
gallon of paint and a brush cost?
b) Members of the senior class held a car wash to
raise funds for their prom. They charged $3 to wash
a car and $5 to wash a pick-up truck or SUV. If they
earned a total of $275 by washing a total of 75
vehicles, how many cars and how many
trucks/SUVs did they wash?
Define the variables:
Define the variables:
x=
x=
y=
y=
Set up two equations in terms of x and y:
Set up two equations in terms of x and y:
Solve using either substitution or elimination
method.
Solve using either substitution or elimination
method.
Price of a gallon of paint =
Number of cars washed =
Price of a brush =
Number of trucks/SUVs washed =
2. Age Problems
a) The sum of Kyla and Brett’s ages are 24. Their
difference in ages is 14. What are the ages of Kyla
and Brett?
b) Juliana is 5 times as old as Jordan and is also 16
years older than Jordan. How old are Juliana and
Jordan?
Define the variables:
Define the variables:
x=
x=
y=
y=
Set up two equations in terms of x and y:
Set up two equations in terms of x and y:
Solve using either substitution or elimination
method.
Solve using either substitution or elimination
method.
Kyla’s age =
Juliana’s age =
Brett’s age =
Jordan’s age =
3. Coin Problems
a) Marcy has a total of 100 dimes and quarters. If the b) Mac’s wallet is full of $5 and $10 bills. He has 25
total value of the coins is $14.05, how many
bills totaling $230. How many of each bill does he
quarters and dimes does she have?
have?
Define the variables:
Define the variables:
x=
x=
y=
y=
Set up two equations in terms of x and y:
Total number of coins:
Set up two equations in terms of x and y:
Total number of bills:
Total value of the coins:
Total value of the bills:
Solve using either substitution or elimination
method.
Solve using either substitution or elimination
method.
Number of quarters =
Number of $5 bills =
Number of dimes =
Number of $10 bills =
4. Mixture Problems
a) A storeowner wants to mix cashews and almonds.
Cashews cost $2 per pound and almonds cost $5 per
pound. She plans to sell 150 pounds of the mixture.
How many pounds of cashews and how many
pounds of almonds should be mixed if one pound of
the mixture costs $3?
b) Suppose a car can run on ethanol and gas and you
have a 15-gallon tank to fill. You can buy fuel that is
either 30% ethanol or 80% ethanol. How many
gallons of 30% ethanol fuel and how many gallons
of 80% ethanol fuel should you mix so the mixture is
40% ethanol fuel?
Define the variables:
Define the variables:
x=
x=
y=
y=
Set up two equations in terms of x and y:
Total weight of mixture:
Set up two equations in terms of x and y:
Total volume of fuel mixture:
Total cost of mixture:
Total amount of ethanol:
Solve using either substitution or elimination
method.
Solve using either substitution or elimination
method.
Number of pounds of cashews =
Number of gallons of 30% ethanol fuel =
Number of pounds of almonds =
Number of gallons of 80% ethanol fuel =