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Math 7
Homework 35
Due Friday, Feb. 3
Find the unit rates for each of the following situations in both possible ways.
Then say which unit rate makes more sense to you.
1. Eight (8) tickets cost $36.
2. A truck can go 75 miles on 15 gallons of gas.
3. Twelve (12) people eat 3 pizzas.
4. Justin can make 5 hexaflexagons in 28 minutes.
The rest of this set is problem solving practice. Please record whatever
attempts you make to solve each problem. There should be evidence of
some effort on every problem, even if you don’t arrive at a solution.
5. If a, b, c, and d each represent any of the positive integers 4, 8, 15, 16,
23, or 42, and each number can be used at most once, what is the largest
a-b
possible value of
?
c-d
1
2
6. Calculate:
4 5
9 12
7. In a cellular phone store, 2/5 of phones are manufactured by Samsung,
1/5 are manufactured by LG, 3/10 are manufactured by AT & T, and the
remaining ten phones are manufactured by other companies. How many
phones in the store are manufactured by Samsung?
8. A government survey reports that 9 out of 10 people brush their teeth at
least once every day. If 14,350 people participated in the survey, how
many of them brush their teeth at least once every day?
9. What is the smallest multiple of 36 that contains only the digits 5 and 0 in
its numeral?
10. Terri produces a sequence of positive integers by following three rules.
She starts with a positive integer, then applies the appropriate rule to the
result, and continues in this fashion.
Rule 1: If the integer is less than 10, multiply it by 9.
Rule 2: If the integer is even and greater than 9, divide it by 2.
Rule 3: If the integer is odd and greater than 9, subtract 5 from it.
A sample sequence: 23, 18, 9, 81, 79, …
Find the 98th term of the sequence that begins 98, 49, …
11. A unit fraction is a fraction that has a 1 in the numerator and a natural
1
number in the denominator. How many ways can you write as a sum
6
of two unit fractions? In other words, find all solutions to the equation
1 1 1
= + , where n and k are natural numbers. How do you know that
6 n k
you found all of them?
12. Now find all ways to write
1
as a sum of unit fractions.
20