Solve the system of equations.
7r + 22k = 101
8r + 20k = 100
What is the value of r?
A. 3 miles
B. 5 miles
C. 7 miles
D.8 miles
MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three
variables using graphical, substitution, and elimination methods.
Solve the system of equations:
30c + 50d = 290
50c + 40d = 310
What is the value of c?
A.
B.
C.
D.
3
4
5
6
MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three
variables using graphical, substitution, and elimination methods.
John is training for a competition in which athletes will run and bike several
miles. If John can run a mile in 7 minutes and bike a mile in 4 minutes, he will be
able to finish the race in 90 minutes. If he can run a mile in 8 minutes and bike a
mile in 3 minutes, he will be able to cover the same distance in just 84 minutes.
In the equations below, r represents the number of miles run, and b represents
the number of miles biked.
7r + 4b = 90
8r + 3b = 84
How many miles will John
run during the race?
A. 6 miles
B. 7 miles
C. 8 miles
D. 12 miles
MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three
variables using graphical, substitution, and elimination methods.
According to government standards, a 100-gram piece of ''extra lean'' meat
must contain 425 or fewer calories. A piece of extra lean meat contains 190
grams of protein and 10 grams of fat, for a total of 850 calories. A second piece
of meat is the same weight, but it is not extra lean.
This piece of meat contains 180 grams of protein and 20 grams of fat, but it has
a total of 900 calories. In the equations below, f represents the number of
calories in a gram of fat, and p represents the number of calories in a gram of
protein.
190p + 10f = 850
180p + 20f = 900
How many calories are
in a gram of protein?
A. 4
B. 5
C. 8
D. 9
MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three
variables using graphical, substitution, and elimination methods.
During a recent campaign, a candidate purchased two television commercials and
one radio commercial for $29,250 in September. In October, she spent $62,250 on
four television ads and three radio ads. In the equations below, r represents the cost
of one radio commercial and t represents the cost of one television commercial.
2t + r = 29,250
4t + 3r = 62,250
What is the cost, in dollars,
of one television commercial?
A.
B.
C.
D.
$ 3,750
$ 12,750
$ 16,500
$ 22,550
MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three
variables using graphical, substitution, and elimination methods.