Algebra 1 Common Core Student Edition, Grade 8-9

Challenge 66. O p e n - E n d e d Find three consecutive integers w ith a sum of 45. Show your work.

67. Cooking A cook buys two identical bags of rice an d uses som e of the rice in each bag
    so that one bag is half full an d the other is one-third full. The cook com bines them
    into one bag, w hich th en contains 3^ cups of rice. How m uch rice was in a full bag?


68. P a i n t i n g Tim can p a in t a h o u se in 6 days. Tara can p ain t the sam e house in 3 days.
    a. W hat fraction of the h o u se can Tim p ain t in one day? W hat fraction of th e house
    can Tara p ain t in one day?
    b. W hat fraction of the house can Tim p ain t in d days? W hat fraction of th e house
    can Tara p ain t in d days?
    c. W hat fraction of the house can Tim an d Tara together p a in t in one day? W hat
    fraction of th e h ouse can Tim a n d Tara together p a in t in d days?
    d. Write an d solve an equ atio n to find th e n u m b e r of days it will take Tim a n d Tara
    to p ain t th e w hole h o u se w orking together.

M P 1, M P 2

Look back at th e inform ation given ab o u t the m onorail on page 79. Let r

represent th e average speed of the m onorail, in feet p er second, betw een the

parking garage an d Term inal A.

a. Write an expression for th e distance th e m onorail travels betw een th e parking

garage an d Term inal A. Then write an expression for th e distance th e m onorail

travels betw een Terminal A an d Terminal B. (Hint: Use th e relationship

distance = rate X time.)

b. Write an equ atio n th at relates th e total distance th e m onorail travels b etw een the

parking garage an d Terminal B to th e two expressions you w rote in p art (a).

c. Solve the eq u a tio n you w rote in p art (b). R ound your answ er to th e n ea rest tenth.

Interpret your solution in term s of the situation.

d. Use your result from p a rt (c) to find the rate of th e m onorail b etw een Terminal A

an d Terminal B.

e. Do the rates you found in p arts (c) a n d (d) m ake sense in term s of th e diagram an d

the tim es given on page 79? Explain.

100 Ch ap t er 2 So l v i n g Eq u a t i o n s