Word Problems Mixture, Distance, Money,
and Integer
(1) When the smaller of two even consecutive integers is
added to 3 times the larger, the
result is 230. Find the smaller integer.
(2) When the smaller of two even consecutive integers is
added to 4 times the larger, the result is 218.
Find the smaller integer.
(3) If 2 times the smaller of two consecutive integers is
added to 6 times the larger, the result is 150 Find the smaller integer.
(4) If 1 times the smaller of two consecutive integers is added to 3 times the
larger, the result is 39. Find the
smaller integer.
(5) The smallest of the three consecutive integers is added
to twice the largest, producing a result 20 less than four times the middle
integer. Find the smallest integer.
(6) The smallest of the three consecutive integers is added
to twice the largest, producing a result 5 less than four times the middle
integer.
Find the smallest integer.
(7) A man has $ 0.70 in dimes and
nickels. He has 8 coins altogether.
How many nickels does she have?
|
|
Number |
Value
in cents |
|
Nickels |
x |
5x |
|
Dimes |
8-x |
10(8-x) |
(8) A man has $ 0.55 in dimes and
nickels. He has 6 coins altogether.
How many nickels does she have?
(9) A woman has $ 0.85 in dimes and
nickels. She has 4 more dimes than
nickels. How many
nickels does she have?
|
|
Number |
Value
in cents |
|
Nickels |
x |
5x |
|
Dimes |
x + 4 |
10(x + 4) |
(10) A woman has $ 1.90 in dimes and
nickels; she has 4 more dimes than
nickels. How many nickels does she have?
(11) A bank teller has some
five-dollar bills and some twenty-dollar bills.
The teller has 4 less of the fives. The total value of the money is $280.00.
Find the number of five-dollar bills that
he has.
|
|
Number |
Value
in dollars |
|
fives |
x |
5x |
|
twenties |
x + 4 |
20(x + 4) |
(12) A bank teller has some five-dollar
bills and some twenty-dollar bills.
the teller has 4
less of the fives. The total value of
the money is $480.00.
Find the number of five-dollar bills that
he has.
(13) A bank teller has some five-dollar
bills and some twenty-dollar bills.
The teller has a total of 24 bills. The total value of the money is $330.00.
Find the number of five-dollar bills that
he has.
|
|
Number |
Value
in dollars |
|
Fives |
x |
5x |
|
Twenties |
24-x |
20(24-x) |
(14) A bank teller has some
five-dollar bills and some twenty-dollar bills.
The teller has a total of 32 bills. The total value of the money is $430.00.
Find the number of five-dollar bills that
he has.
(15) A bank teller has some five-dollar
bills and some twenty-dollar bills.
The teller has 4 more of the
twenties. The total value of the money
is $305.00.
Find the number of five-dollar bills that
he has.
|
|
Number |
Value
in dollars |
|
fives |
x |
5x |
|
twenties |
x + 4 |
20(x + 4) |
(16) A bank teller has some five-dollar
bills and some twenty-dollar bills.
The teller has 4 more of the
twenties. The total value of the money
is $505.00.
Find the number of five-dollar bills that
he has.
(17) Caroline needs a 3 % solution. How
many liters of a 1 % solution
should she add to 2 liters of a 32 % solution to get a 3 %
solution?
|
|
start |
add |
End up |
|
amount |
2 |
x |
x+2 |
|
percent |
32 |
1 |
3 |
(18) Caroline needs a 7 % solution. How
many liters of a 1 % solution
should she add to
18 liters of a 29 % solution to get a 7 % solution?
(19) How many gallons of pure alcohol
solution should be added to
63 gal of a 32 % alcohol
solution to make a 37 % solution?
|
|
start |
add |
End up |
|
amount |
63 |
x |
x+63 |
|
percent |
32 |
100 |
37 |
(20) How many gallons of pure alcohol
solution should be added to
12 gal of a 12 % alcohol
solution to make a 34 % solution?
(21) How many gallons of 16 % alcohol
solution should be added to
30 gal of a 45 % alcohol
solution to make a 21 % solution?
|
|
start |
add |
End up |
|
amount |
30 |
x |
x+30 |
|
percent |
45 |
16 |
21 |
(22) How many gallons of 13 % alcohol
solution should be added to
20 gal of a 43 % alcohol
solution to make a 23 % solution?
(23) How many gallons of 51 % alcohol
solution should be added to
some of a 57 %
alcohol solution to make a 438 gal of a 55 % solution?
|
|
start |
add |
End up |
|
amount |
438-x |
x |
438 |
|
percent |
57 |
51 |
55 |
(24) How many gallons of 16 % alcohol solution
should be added to
some of a 78 %
alcohol solution to make a 576 gal of a 16 % solution?
(25)
How much pure water should she add to make
the 8 % solution?
|
|
start |
add |
End up |
|
amount |
2 |
x |
x+2 |
|
percent |
28 |
0 |
8 |
(26)
solution. How much pure water should she add to make
the 7% solution?
(27) Mary and David are 833 miles
apart and are heading toward each other to
meet for dinner.
Mary is traveling at 54 mph and David is traveling at 65 mph.
how longs before
they meet?
|
|
Distance |
Rate |
Time |
|
Mary |
54x |
54 |
x |
|
David |
65x |
65 |
x |
(28) Mary and David are 1240 miles apart
and are heading toward each other to
meet for dinner.
Mary is traveling at 51 mph and David is traveling at 73 mph.
How longs before they meet?
(29) David and Caroline leave buoy 15 traveling
in opposite directions.
If David travels at 66 mph and Mary
travels at 52 mph, then how long will it be
before they are
1180 miles apart?
|
|
Distance |
Rate |
Time |
|
Mary |
52x |
52 |
x |
|
David |
66x |
66 |
x |
(30) David and
Caroline leave buoy 15 traveling in opposite directions. If David
travels at 66 mph
and Mary travels at 77 mph, then how long will it be before
they are 572
miles apart?
(31) Fred leaves John's house and drives
toward
hours later and
drives the same route at 45 mph. How
long will it take Kim to
overtake Fred?
|
|
Distance |
Rate |
Time |
|
Kim |
45x |
45 |
x |
|
Fred |
27(x+2) |
27 |
x+2 |
(32) Fred leaves john's house and drives
toward
hours later and
drives the same route at 42 mph. How
long will it take Kim to
overtake Fred?