# Solutions

Awesome job on today’s word problem! Are you ready to check your answer? Look below to see if your solution matches ours.

**Lower Elementary:***Answer: *3 grams*Solution: *To find the weight of the missing part of the charm, we subtract 2 ^{1}⁄_{2} grams from 5 ^{1}⁄_{2} grams. We can do this by splitting 2 ^{1}⁄_{2} grams into 2 grams and ^{1}⁄_{2} of a gram. If we subtract 2 grams first, we get 5 ^{1}⁄_{2} – 2 = 3 ^{1}⁄_{2} grams. Next, we subtract the half to get 3 ^{1}⁄_{2} – ^{1}⁄_{2} = 3 grams. So, the missing part of the charm weighs 3 grams.

**Upper Elementary:***Answer: *6 ounces*Solution: *First, we need to know what fractional part of the sandwich is uneaten. Since Benjamin ate ^{3}⁄_{10} and Jerry ate ^{2}⁄_{5} = ^{4}⁄_{10}, they ate ^{7}⁄_{10} of the baguette in total. That means that the remaining ^{10}⁄_{10} – ^{7}⁄_{10} = ^{3}⁄_{10} of the baguette weighs 4 ^{1}⁄_{2} ounces. Each tenth of the baguette therefore weighs 4 ^{1}⁄_{2} ÷ 3 = 1 ^{1}⁄_{2} ounces. So, since Jerry ate ^{4}⁄_{10} of the baguette, his piece was 1 ^{1}⁄_{2} × 4 = 6 ounces.

**Middle School:***Answer: *$5.26*Solution: *The cost before tax of the pie and coffee is $1.50 + $2.50 = $4.00, so the cost after tax is $4.00 + ($4.00 × 0.065) = $4.26. With the tip included, Dale spends $4.26 + $1.00 = $5.26.

**Algebra and Up:***Answer: *3,000 radians per minute*Solution: *Since a radian has an arc length equal to the radius, each radian that the saw rotates causes 3 feet of the edge of the blade to strike the tree. So, to find the number of radians that would cause 9,000 feet of the edge of the blade to strike the tree, we divide 9,000 ÷ 3 = 3,000. The rate at which the blade rotates is 3,000 radians per minute.