Arithmetic - Level 1

(1) What fractional part of 72 is 16?

(2) How many more cents per item is 3 items for $10 than 2 items for $5?

Express your answer to the nearest whole number.

(3) A 2-cup mixture is 13 our and 2

3cornmeal. If 1 cup of our is added to the

2-cup mixture, what fraction of the new 3-cup mixture is our? Express your answer as a

common fraction.

(4) How many 32-passenger buses will be needed to take 200 students on a �eld

trip?

(5) In 1983, Norman Johnson set a record by slicing each inch of a 12-inch

cucumber into 22 pieces. It took him 13.4 seconds. When Norman �nished, into how many

pieces was the cucumber divided?

(6) If Heidi can paint a wall in 45 minutes, what fractional part of the wall can

she paint in 9 minutes?

(7) A ferry trip departs from the ferry dock every 15 minutes. Yesterday the

�rst ferry trip left at 8 a.m. and the last ferry trip left at 5 p.m. How many ferry trips left

from the ferry dock yesterday?

(8) If the current time is 7:03 a.m. on a 12-hour clock, what time will it be in

553 minutes? (Include units a.m. or p.m.)

(9) A pitcher contains 412cups of water. A 1

3-cup scoop is used to transfer

water from the pitcher to a bowl. How many scoops are needed until the bowl has more

water than the pitcher?

(10) Kaya ate 60 cookies over a �ve-minute period. On average, how many

cookies did she eat each minute?

(11) The sum of the squares of two positive integers is 73. What is the sum of

the two positive integers?

(12) What is the positive di�erence between 25 and 52?

(13) Francisco starts with the number 5, doubles it, adds 1, doubles the result,

adds 1, doubles the result, adds 1, and continues this pattern of two alternating

calculations. Phong, meanwhile, starts with 5, adds 1, doubles the result, adds 1, doubles

the result, adds 1, doubles the result, and continues this pattern of two alternating

calculations. They each do eight total calculations. What is the positive di�erence of their

�nal results?

(14) If April 4 is the �rst day of a new project, and June 6 is the last day, for how

many days did the project run?

(15) Sean had a temperature of 99:6�F at 3 p.m. Five hours later his

temperature was 102:4�F. By how many degrees Fahrenheit did his temperature rise during

those �ve hours? Express your answer as a decimal to the nearest tenth.

(16) In 4 baseball games, a batter had 3 hits in 5 times at bat, 1 hit in 4 times at

bat, 2 hits in 5 times at bat, and no hits in 4 times at bat. What was her batting average

for the four games? Express your answer as a decimal rounded to the nearest thousandth.

(17) A bottling plant �lls 0.5-liter bottles from a 56-liter tank. A at consists of

24 bottles. How many complete ats can be �lled from a single tank?

(18) At 2:30 p.m. during a long drive, Bobbi asks her parents, \Are we there

yet?" Her mother responds, \We will be there in 7200 seconds." If Bobbi's mother is

correct, at what time in the afternoon will they arrive at their destination?

(19) April wants to paint three walls of her bedroom. The walls are each 90

square feet. Paint is only sold in whole quarts, and each quart of paint will cover 100 square

feet. How many quarts of paint must she purchase to have su�cient paint for this job?

(20) Four pencils and a pen cost $3:00. If a pen costs $1, how many dollars will

12 pencils and two pens cost?

(21) Marian wishes to buy a new computer that will cost her $300. She receives

$5 per hour for watching her younger brother and $4 per hour for helping her mother with

chores. Each week she watches her brother for four hours and helps her mother with chores

for 10 hours. How many full weeks must she work to earn enough money to buy the

computer?

(22) Find, in simpli�ed fraction form, the reciprocal of 3.2.

(23) Three friends each ordered a large cheese pizza. Shauntee ate 23of her

pizza, Carlos ate 89of his pizza and Rocco ate 26

27of his pizza. If the remaining portions

from the three pizzas are put together, what fraction of a large pizza do they make?

Express your answer as a common fraction.

(24) What common fraction is exactly half-way between 23and 4

5?

(25) Sugar can be purchased in either 3-pound or 5-pound bags. A 3-pound bag

of sugar costs $2:10 while a 5-pound bag costs $3:39. When spending the least amount

of money possible to purchase exactly 34 pounds of sugar, how many 5-pound bags of

sugar will be purchased?

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Answer Sheet

Number Answer Problem ID

1 2/9 C1012

2 83 cents 4504

3 5/9 CD312

4 7 0CB02

5 264 D14C

6 1/5 of a wall 03012

7 37 trips CCA

8 4:16 p.m. CD5B

9 7 scoops BBA

10 12 cookies C021

11 11 DC31

12 7 5C11

13 15 D342

14 64 days BDD

15 2.8 degrees B1D1

16 0.313 AB412

17 4 ats CCD

18 4:30 p.m. A051

19 3 quarts BC012

20 8 dollars 40C

21 5 full weeks 12

22 5/16 3BB12

23 13/27 2142

24 11/15 B1312

25 5 5-pound-bags C04B

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Solutions

(1) 2/9 ID: [C1012]

The fractional part of 72 that 16 is can be found by simplifying the fraction 16=72. 16 and

72 both contain a factor of 8, so we have that 1672

= 2�89�8

=2

9.

(2) 83 cents ID: [4504]

Three items for ten dollars is 1000=3 = 33313cents per item. Two items for �ve dollars is

500=2 = 250 cents per item. The di�erence is 33313� 250 � 83 cents.

(3) 5/9 ID: [CD312]

The amount of our originally in the 2-cup mixture is 13� 2 = 2

3cups. When a cup is added,

there are 53cups of our. This is 5

3� 3 =

5

9of the 3-cup mixture.

(4) 7 ID: [0CB02]

Consider the fact that 20032

= 6:25. If 6 buses are used, not all students would �t. If 7 buses

are used, all students would �t, with leftover space. Thus the answer is 7 .

(5) 264 ID: [D14C]

Each inch is cut into 22 pieces, so 12 inches are cut into 12� 22 = 264 pieces.

(6) 1/5 of a wall ID: [03012]

Since 9 minutes is 1=5 of 45 minutes, we can �nd the fractional part of a wall that Heidi

can paint in 9 minutes by dividing the amount of wall that Heidi can paint in 45 minutes by

5. Since Heidi can paint a whole wall in 45 minutes, it follows that she can paint1

5of a

wall in 9 minutes.

(7) 37 trips ID: [CCA]

Every hour there are 4 ferry departures. Since there are 9 hours between 8 a.m. and 5

p.m., there were 36 departures between the 8 a.m. hour and the 4 p.m. hour, inclusive.

Including the one departure at 5 p.m., there were 36 + 1 = 37 departures total.

(8) 4:16 p.m. ID: [CD5B]

Since 60 � 9 = 540 minutes is 9 hours, 553 minutes is 9 hours and 13 minutes. Thus, 553

minutes after 7:03 a.m. is 4:16 p.m. .

(9) 7 scoops ID: [BBA]

The bowl has more water than the pitcher when it has more than4 1

2

2= 21

4cups of water.

Since2 1

4

1

3

= 94� 31= 27

4= 6:75, it takes 7 scoops for the water in the bowl to be more than

the water in the pitcher.

(10) 12 cookies ID: [C021]

The number of cookies Kaya ate each minute is equal to the total number of cookies she

ate divided by the time she ate them in, or 60=5 = 12 cookies each minute.

(11) 11 ID: [DC31]

If m2 + n2 = 73, then either m2 or n2 is greater than 73/2. Without loss of generality,

suppose that n2 is greater than 73/2. Since n2 is also less than 73, the only possible values

for n are n = 7 and n = 8, which imply m =p73� 49 =

p24 and

p73� 64 =

p9 = 3,

respectively. Since only the second value of m is an integer, we have m + n = 3 + 8 = 11 .

(12) 7 ID: [5C11]

25 � 52 = 32� 25 = 7 .

(13) 15 ID: [D342]

The arithmetic is simple enough that we can just write down the results of the calculations.

Francisco's calculations give 5, 10, 11, 22, 23, 46, 47, 94, 95 (nine numbers, but only eight

calculations since the 5 was given). Phong's give 5, 6, 12, 13, 26, 27, 54, 55, 110. The

positive di�erence is 15 .

(14) 64 days ID: [BDD]

April has 30 days, so 30� 4 + 1 = 27 days of the project were spent in April. May has 31

days, so 31 days of the project were spent in May. 6 days were spent in June. Adding

everything, the total number of days is 27 + 31 + 6 = 64 .

(15) 2.8 degrees ID: [B1D1]

Sean's temperature rose 102:4� 99:6 = 2:8 degrees.

(16) 0.313 ID: [AB412]

Respectively, the ratios of hits to times at bat for each game are 35= 0:6, 1

4= 0:25,

25= 0:4, and 0. The average of these numbers is 0:6+0:25+0:4+0

4= 0:3125, which rounds to

0:313 .

(17) 4 ats ID: [CCD]

There are 56=:5 = 112 bottles in a tank, and since 96 = 4 � 24, there are 4 complete ats

that can be �lled from a tank.

(18) 4:30 p.m. ID: [A051]

Multiply 7200 seconds by(1 min.60 sec.

) (1 hr.

60 min.

)to �nd that they will arrive in 2 hours. Two

hours after 2:30 p.m. is 4:30 p.m. .

(19) 3 quarts ID: [BC012]

April wants to paint 90�3 = 270 square feet. The smallest multiple of 100 which is greater

than or equal to 270 is 300, so she needs to purchase 300=100 = 3 quarts of paint.

(20) 8 dollars ID: [40C]

Four pencils and a pen cost $3:00. If we triple this, we see that twelve pencils and three

pens cost $9:00. We want to �nd the price of twelve pencils and two pens. We are also

given that the cost of one pen is $1:00. Subtracting this, we �nd that twelve pencils and

two pens costs $8:00 .

(21) 5 full weeks ID: [12]

The total amount of money Marian earns each week is

4($5) + 10($4) = $60

so the number of weeks necessary is $300$60

= 5 .

(22) 5/16 ID: [3BB12]

We know that 3:2 = 3 + :2 and since :2 = 1=5, we have that 3:2 = 315. Converting this

mixed number into a common fraction, we have that 315= 3�5+1

5= 16

5, so its reciprocal is

5

16.

(23) 13/27 ID: [2142]

The remaining fractions of pizzas are 1=3; 1=9, and 1=27. Adding with a common

denominator of 27 gives9

27+

3

27+

1

27=

13

27.

(24) 11/15 ID: [B1312]

The average of two numbers is exactly half-way between them. Therefore,

12

(23+ 4

5

)=

11

15is half-way between 2

3and 4

5.

(25) 5 5-pound-bags ID: [C04B]

First, we need to see if the 3 or 5 pound bag is cheaper per pound of sugar. The 3 pound

bag is 2:10=3 = :70 per pound. A 5 pound bag at that price would cost 5 � :70 = 3:50, so

clearly the 5 pound bag is cheaper. This means we need to purchase as many 5 pound bags

as possible.

If we bought 7-�ve pound bags, we would purchase 35 pounds, too much sugar. It is not

possible to buy 6-�ve pound bags, as this will leave 4 extra pounds. If we buy 5-�ve pound

bags, this will be a total of 5 � 5 = 25 pounds, leaving 9 pounds remaining. We can then

purchase 3-three pound bags, to get exactly 34 pounds of sugar as cheap as possible. Our

answer is 5 -�ve pound bags.

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