#1

Sydney took a math test that had 32 questions on it and scored 111 points. Each correct answer was awarded 5 points and for each wrong answer two points were deducted. How many questions did she miss on her test?

Sydney took a math test that had 32 questions on it and scored 111 points. Each correct answer was awarded 5 points and for each wrong answer two points were deducted. How many questions did she miss on her test?x correct answers

y incorrect answers

x y 32E1E2 5x 2y 111

7y 49y 7She missed 7 questions.She missed 7 questions.

5x 5y 160

5x 2y 111

Define variables:

Let x be the larger numberLet y be the smaller number

Write two equations

E1

E2

x y 43

x 3y 1 21

Solve the system

3y 1 y 43

2y 42y 21

One number is 43 less than another number. The larger number is one more than three times the smaller number. What is the smaller of the two numbers?

One number is 43 less than another number. The larger number is one more than three times the smaller number. What is the smaller of the two numbers?

#2

Haley was going to be paid to unpack a box of 125 delicate crystal ornaments. She would be paid 75 cents for each ornament unpacked, but would be charged $2.50 for any that she broke. After finishing the job she was paid $74.25. How many ornaments did she break?

Haley was going to be paid to unpack a box of 125 delicate crystal ornaments. She would be paid 75 cents for each ornament unpacked, but would be charged $2.50 for any that she broke. After finishing the job she was paid $74.25. How many ornaments did she break?

Let xx be the number of ornaments unpacked successfully.

Let y be the number of ornaments broken

#3#3

x y 125

0.75x 2.50y 74.25 75x 250y 7425

75x 75y 9375

325y 1950y 6

She broke 6 ornaments. She broke 6 ornaments.

#4

Will set a school record by scoring 30 points in his basketball game. What was amazing is that he scored all his points without a single free-throw. Out of the 13 baskets that he made, how many were 3-point shots?

Will set a school record by scoring 30 points in his basketball game. What was amazing is that he scored all his points without a single free-throw. Out of the 13 baskets that he made, how many were 3-point shots?x 2-point shots

y 3-point shots

x y 13E1E2 2x 3y 30

y 4He made 4, 3-pointers.He made 4, 3-pointers.

2x 2y 26

2x 3y 30

100 25

#5#5

Jackie’s coin purse had only dimes and quarters in it. There were 5 more dimes than quarters, and the total amount of money was $7.85. How many dimes were in the purse?

Jackie’s coin purse had only dimes and quarters in it. There were 5 more dimes than quarters, and the total amount of money was $7.85. How many dimes were in the purse?

x number of dimes

y number of quarters

x y 5

0.10x 0.25y 7.85 10x 25y 785

25x 25y 125

35x 910x 2626 dimes26 dimes