1. Choose the correct answer.

Elena bought 320 tropical fish for a museum display. She bought 7 times as many triggerfish as parrotfish. How many of each type of fish did she buy?

Which is a system of equations to model the problem if x represents the number of parrotfish Elena bought and y represents the number of triggerfish she bought?

A.

x + y = 320

y = 7x

B.

x + 7y = 320

y = 7x

C.

x – y = 320

y = 7x

D.

x + y = 7

y = 320x

2. Michael and Kathryn bowl together and their combined total score for one game was . Michael’s score was 70 less than twice Kathryn’s. What were their scores?

Which is a system of equations to model the problem if x represents Kathryn’s score and y represents Michael’s score?

A.

x + y = 70

y = 2x – 425

B.

x – y = 425

y = 2x – 70

C.

x + y = 425

y = 2x – 70

D.

x + y = 425

y = 2x + 70

3. David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.

How long will each piece of hose be?

Shorter piece:______ft

Longer piece:______ ft

4. Admission for a movie is $8 for children and $12 for adults. On a certain day, 3200 people attend the movie theater and $33,040 is collected.

How many children and how many adults attended the movies?

children. __?____

adults. ____?____

5. A collection of quarters and dimes is worth $12.40. There are 67 coins in all.

How many of each coin are there?

quarters. ___?_____

dimes. ___?____

**1. A. **x parrot fish + y triggerfish = 320 total fish.

y = 7x shows that there are 7 times as many triggerfish.

**2. C**

x + y shows a total score of 425.

y = 2x - 70 shows that Michael’s score, y, is 70 less (minus) than twice Kathryn’s

**3**. write two equations

x + y = 27 total feet

2x + 3 = y

Substitute 2x + 3 for y in the first equation

x + (2x + 3) = 27

3x + 3 = 27

3x = 24

**x = 8**

Substitute 8 in to either equation to find the other length.

8 + y = 27

y = 19

**The shorter piece is 8 and the longer piece is 19**

**4.**x + y = 3200 people -> y = 3200-x

8x + 12y = 33,040 dollars

8x + 12(3200 - x) = 33040

8x + 38400 - 12x = 33040

-4x = -5360

**x = 1340 (1340 children)**

1340 + y = 3200

**y = 1860 adults**

**5.**I don’t think the numbers for this were put in correctly because I get a decimal and a negative number when I solve for it but hopefully if you do get the correct cost/amount of coins you will understand this well enough to do it on your own.