Algebra 1
Problem Solving
Name ___________________________
1. Three boys, Josh, Hans, and Simon, are sitting around on a farm with nothing to do. They walk into the barn and
notice a scale used to weigh cattle. They decide to weigh themselves. Unfortunately, the scale begins at 100 kg. The
problem is that none of them weigh more than 100 kg. They decide to weigh themselves in pairs. Josh was sure that he
weighed the most.
Hans & Simon = 132 kg
Simon & Josh = 151 kg
Josh & Hans = 137 kg
How much did they each weigh?
2. You have $1.65 made up of pennies, nickels, and dimes. Half of the coins are nickels. How many coins of each do you
have?
3. The six hundred members of the ninth-grade class are seated in rows, each of which contains the same number of
chairs, and every chair is occupied. If five more chairs were in each row, everyone could be seated in four fewer rows.
How many chairs are in each row?
4. What are the next two numbers in the sequence?
11, 31, 71, 91, 32, 92, 13, 73, 14, 34, 74, 35, 95, …
5. How many rectangles of any size are on an 8x8 checkerboard?
6. A caterpillar will gain 2 grams of weight every day eating as much as possible. Not eating results in losing 3 grams of
weight per day. If the caterpillar gained 5 grams over 20 days, how many days were spent not eating?
7. At your favorite ice cream parlor, you decide to order a two-scoop cone. There are 14 different flavors of ice cream
and three different types of cones. How many different types of two-scoop ice-cream cones can you order?
8. I have a very strange algebra teacher that collects old mathematics books. One day, I asked how many old math
books were in the collection. Being a math teacher, the response was, “If I divide the books into two unequal whole
numbers, then 64 times the difference between the two numbers equals the difference between the squares of the two
numbers.” How many old math books does my algebra teacher have?