Download 2 Math Challengers Team Training Worksheet I. Alicia has 5 dollars

2nd Math Challengers Team Training Worksheet
I.
Alicia has 5 dollars less than Beti, and Cecille has as much money as Alicia and Beti have
between them. Altogether, the three people have a total of 270 dollars. How many dollars
does Alicia have?
II.
Two pencils and three erasers cost $10. Three pencils and two erasers cost $14. How much
do five pencils and one eraser cost altogether?
III.
The sum of eight times the reciprocal of two less than a number and two times the reciprocal
of ten less than two times that number is 3. What is the sum of all of the possible numbers?
IV.
Alfie gave B one-half of the loonies Alfie had, and then 7 more. Alfie then gave C one-half of
the loonies he had left, and then 7 more. After that, Alfie had no loonies left. How many
loonies did Alfie start out with?
1. The cost of sending a parcel is $4.00 for the first kilogram, and $0.60 for each additional kg. A
certain parcel weighs a whole number of kg, and costs $40.00 to send. How many kg does the
parcel weigh?
2nd Math Challengers Team Training Worksheet
2. A rectangular field is 50% longer than it is wide. The perimeter of the field is 300 meters. What
is the area of the field in square meters?
3. Beta has twice as many pennies as Alpha. Gamma has three times as many pennies as Beta.
Between the three of them, they have fewer than 80 pennies. What is the largest possible
number of pennies Beta can have?
4. A string of length 120 centimeters is cut into three parts whose lengths are proportional to 4,5,
and 6. What is the length, in centimetres, of the longest part?
5. The sum of two positive whole numbers is 144. If the larger of the two numbers is divided by
the smaller, the quotient is 3 and the remainder is 12. What is the smaller of the two numbers?
6. When we increase 200 by a certain percent, we get the same results as when we decrease 300
by the same percent. What is that percent?
7. A loonie (1 dollar coin) weighs 4 times as much as a dime (10 cent coin). Bag A contains only
loonies, bag B contains 5 times as many dimes as loonies, but no other coins or notes. Bags A
and B have exactly the same weight. If bag A contains 45 dollars’ worth of loonies, what is the
value, in dollars, of the dimes in Bag B?
2nd Math Challengers Team Training Worksheet
8. Alva had a total of $50 in 1-dollar coins and 2-dollar coins. If the 1-dollar coins were 2-dollar
coins and the 2-dollar coins were 1-dollar coins, Alva would have $70. What is the total
number of coins that Alva has?
9. Albert gave Beth as many pennies as Beth had. Then Beth gave Albert as many pennies as
Albert still had. Finally, Albert gave Beth as many pennies as Beth still had. After these three
transactions, Albert had 0 pennies, and Beth had 96. How many pennies did Beth start out
with?
10. In the election for Student Council president, there were four candidates, A, B, C, and D. Each
of the 1000 students voted for one and only one of these candidates. Candidate A got 40 more
votes than candidate B, 200 votes more than C, and 300 more votes than D. How many votes
did A get?
11. What is the smallest possible value of n2-17n+100 as n ranges over the integers?
12. If x and y are real numbers such that x + y = 11 and xy = 13, what is the value of x2 + y2?
13. Let x ~ y = x2 − 2y2 . What is the value of 3 ~ (2 ~ 1)?
2nd Math Challengers Team Training Worksheet
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14. What is the product of the solutions of the equation √4 − 𝑥 = 4 − 𝑥 ?
15. Unbelievably, George perfected a fruit-growing system where there was never any variation
in the weight of each particular fruit. He weighed 3 apples and 2 oranges and found that
together they weighed 38 ounces. To double check, he weighed 5 apples and 3 oranges and
found that together they weighed 60 ounces – exactly what he expected. How many ounces
does each orange weigh?
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1 2
16. Given that (𝑥 2 + 𝑥 2 ) = 100, what is the value of (𝑥 2 − 𝑥 2 ) ?
17. Starting with 1, Zephyr found the sum of the first n positive integers, but accidentally forgot
to add one of the numbers, thus getting a sum of 643. What is the value of n?
18. The parabolas y = 2x 2 + 14 and y = x 2 − 4x + 11 intersect at the points (a, b) and (c, d). What is
the value of a + b + c + d?
19. The combined cost of one candy, one chocolate bar, and one cookie is $2.71. The combined
cost of one candy, one chocolate bar, and three cookies is $5.25. The combined cost of one
candy, two chocolate bars, and three cookies is $6.36. What is the cost of one candy? Give the
answer in $, correct to two decimal places.