11. On a team, 6 girls and 3 boys scored a total of 72 points. The difference between the number of points scored by the 6 girls and the number of points scored by the 3 boys is 36. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
12. Reasoning Which method is the most efficient algebraic method to solve the system of equations?
table with 2 rows and 2 columns , row1 column 1 , x , column 2 equals 4 y plus 12 , row2 column 1 , negative 3 x minus 3 y , column 2 equals minus 12 , end table
A. The substitution method, because one of the equations is in “y=” form.
B. The substitution method, because one of the equations is in “x=” form.
C. The addition method, because the x-terms are additive inverses.
D. The addition method, because the y-terms are additive inverses.
13. Error Analysis Lois claims the solution to the system of equations is (−1, −4).
table with 2 rows and 2 columns , row1 column 1 , 5.5 x plus 5.3 y , column 2 equals minus , 27.3 , row2 column 1 , 4.1 x minus 5.3 y , column 2 equals minus , 11.1 , end table
a. Solve the system of equations using addition.
b. What mistake might Lois have made?
A. She used the opposite sign for y in the answer.
B. She used the opposite sign for x in the answer.
C. She exchanged x and y in the answer.
D. She used the opposite sign for x and y.
14. Trains Two trains, Train A and Train B, weigh a total of 312 tons. Train A is heavier than Train B. The difference of their weights is 170 tons. What is the weight of each train?
15. Multiple Representations Solve the system of equations using addition.
table with 2 rows and 2 columns , row1 column 1 , x minus 7 y , column 2 equals 11 , row2 column 1 , x plus 7 y , column 2 equals minus 17 , end table
a. Which of the following shows the correct solution, written two ways?
A. (−3, −2), x=−2 and y=−3
B. (−2, −3), x=−2 and y=−3
C. (−3, −2), x=−3 and y=−2
D. (11, −17), x=−17 and y=11
E. (11, −17), x=11 and y=−17
F. (−7, 7), x=7 and y=−7
b. Draw a graph to show the solution in a third way.
16. Two balloons, Balloon A and Balloon B, have a total volume of 3 fifths gallons. Balloon A has a greater volume than Balloon B. The difference of their volumes is 1 fifth gallons. What is the volume of each balloon? Simplify your answers.
17. Solve the system using addition.
table with 2 rows and 2 columns , row1 column 1 , 6 x plus 9 y , column 2 equals 6 , and 3 fifths , row2 column 1 , negative 6 x plus y , column 2 equals minus , 3 fifths , end table
18.
a. Challenge Use addition to solve the system. Then solve the system again, this time using the substitution method.
table with 2 rows and 2 columns , row1 column 1 , 1 , and 3 fourths , x plus y , column 2 equals 2 , and 3 sixteenths , row2 column 1 , 1 fourth , x minus y , column 2 equals minus 1 , and 11 over 16 , end table
b. Was one method easier than another? Explain.
19. Challenge On a fishing trip, Reba catches two types of fish. Each of Fish A weighs 7 ninths pound and each of Fish B weighs 1 ninth pound. The total weight of all the fish is 5 , and 7 ninths pounds. The difference in weight of all of Fish A and all of Fish B is 5 , and 1 ninth pounds. Find how many fish of each type Reba caught.