Score 18/18
You passed this Milestone
18 questions were answered correctly.
UNIT 3 — MILESTONE 3
1
The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below.
Betty needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $50.73. At Supermarket B, she would pay $51.63.
Which of the following system of equations represents this situation?
,RATIONALE
In general, the equation to represent the total cost of buying bread and milk would be the sum of the cost for bread and co
cost of bread and milk, first define variables to represent the amount of bread and milk.
Here, will represent bread, and will represent milk. Both and will be multiplied by their respective prices.
At Store A, a loaf of bread costs , and a gallon of milk costs . We also know that the total cost at Store A is
of Store A would be expressed with this equation. We can construct a similar equation for Store B.
At Store B, bread cost per loaf, and milk costs per gallon. We also know that the total cost at Store B is
Store B would be expressed with this equation.
This is the system of equations to represent the costs of bread and milk at Store A and B.
CONCEPT
Writing a System of Linear Equations
2
On his way home from the school board meeting, Keith fills up his car. He likes the idea of using gasoline with ethanol, but thinks his car can only handle 40% ethanol.
use regular gas with 10% ethanol or E85 fuel with 85% ethanol.
How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol?
, 4 gallons of regular gas with 10% ethanol;
6 gallons of E85 fuel with 85% ethanol
2 gallons of regular gas with 10% ethanol;
8 gallons of E85 fuel with 85% ethanol
8 gallons of regular gas with 10% ethanol;
2 gallons of E85 fuel with 85% ethanol
6 gallons of regular gas with 10% ethanol;
4 gallons of E85 fuel with 85% ethanol
RATIONALE
We will use the variables and to represent the types of fuel: represents the gallons of ethanol gas, and represents the gall
equation is the total amount of gas Keith will use to fill up his car.
He can use the two types of fuel, and together, he puts gallons of gas in his car, so . The second equation will represent
from the two fuels.
The coefficient to is because that is the ethanol fuel. The coefficient to is because that is the ethanol fuel. F
gallons of ethanol, which can be expressed as times . We now need to solve this system of equations.
Since we have two equations that represent this equation, one way to solve is to use substitution to rewrite one variable in terms of the
variable at a time. Let's take a look at the second equation.
In equation , subtracting from both sides gives us . We can use this in the other equation to write as .
This is the other equation in the system, but has been replaced with an equivalent expression of . Now this is a single-variabl
solve for . First, distribute into .
, times is and times is . Next, evaluate the multiplication on the right side.
times is . Now, combine like terms on the left side.
We can combine and to get . Next, subtract from both sides.
minus equals . Finally, divide both sides by .
divided by is equal to . Because represents the gallons of ethanol fuel, Keith fills his car with gallons of
This also means he uses gallons of ethanol fuel because he uses gallons total.
CONCEPT
Solving Mixture Problems using a System of Equations
3
Examine the following table.
Which graph corresponds to this table?
You passed this Milestone
18 questions were answered correctly.
UNIT 3 — MILESTONE 3
1
The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below.
Betty needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $50.73. At Supermarket B, she would pay $51.63.
Which of the following system of equations represents this situation?
,RATIONALE
In general, the equation to represent the total cost of buying bread and milk would be the sum of the cost for bread and co
cost of bread and milk, first define variables to represent the amount of bread and milk.
Here, will represent bread, and will represent milk. Both and will be multiplied by their respective prices.
At Store A, a loaf of bread costs , and a gallon of milk costs . We also know that the total cost at Store A is
of Store A would be expressed with this equation. We can construct a similar equation for Store B.
At Store B, bread cost per loaf, and milk costs per gallon. We also know that the total cost at Store B is
Store B would be expressed with this equation.
This is the system of equations to represent the costs of bread and milk at Store A and B.
CONCEPT
Writing a System of Linear Equations
2
On his way home from the school board meeting, Keith fills up his car. He likes the idea of using gasoline with ethanol, but thinks his car can only handle 40% ethanol.
use regular gas with 10% ethanol or E85 fuel with 85% ethanol.
How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol?
, 4 gallons of regular gas with 10% ethanol;
6 gallons of E85 fuel with 85% ethanol
2 gallons of regular gas with 10% ethanol;
8 gallons of E85 fuel with 85% ethanol
8 gallons of regular gas with 10% ethanol;
2 gallons of E85 fuel with 85% ethanol
6 gallons of regular gas with 10% ethanol;
4 gallons of E85 fuel with 85% ethanol
RATIONALE
We will use the variables and to represent the types of fuel: represents the gallons of ethanol gas, and represents the gall
equation is the total amount of gas Keith will use to fill up his car.
He can use the two types of fuel, and together, he puts gallons of gas in his car, so . The second equation will represent
from the two fuels.
The coefficient to is because that is the ethanol fuel. The coefficient to is because that is the ethanol fuel. F
gallons of ethanol, which can be expressed as times . We now need to solve this system of equations.
Since we have two equations that represent this equation, one way to solve is to use substitution to rewrite one variable in terms of the
variable at a time. Let's take a look at the second equation.
In equation , subtracting from both sides gives us . We can use this in the other equation to write as .
This is the other equation in the system, but has been replaced with an equivalent expression of . Now this is a single-variabl
solve for . First, distribute into .
, times is and times is . Next, evaluate the multiplication on the right side.
times is . Now, combine like terms on the left side.
We can combine and to get . Next, subtract from both sides.
minus equals . Finally, divide both sides by .
divided by is equal to . Because represents the gallons of ethanol fuel, Keith fills his car with gallons of
This also means he uses gallons of ethanol fuel because he uses gallons total.
CONCEPT
Solving Mixture Problems using a System of Equations
3
Examine the following table.
Which graph corresponds to this table?
