Lower Elementary:
Question: Gary and May decide to have a contest to see who can pick the most strawberries. They each had two baskets. Gary has 45 strawberries in one of his baskets and 64 strawberries in the other. May has 42 strawberries in one of her baskets and 68 strawberries in the other. Who picked more strawberries?
Answer: May, she picked 1 more strawberry than Gary
Solution: To see who picked more strawberries, we have to find the total amount that each person picked. Gary picked 45 + 64 = 109 strawberries. May picked 42 + 68 = 110 strawberries. So, May picked 1 more strawberry than Gary.
Upper Elementary:
Question: Becky baked some cookies. Half of the cookies she baked are chocolate chip, 1/6 of the cookies are raisin, and the remaining 12 cookies are peanut butter. How many total cookies did Becky bake?
Answer: 36 cookies
Solution: One way to solve this problem is to first find the fractional part that the peanut butter cookies represents, then use that fractional part to find the whole amount of cookies baked. To find a part, take the whole and subtract the sum of the other parts. Half of the cookies were chocolate chip and 1/6 of the cookies were raisin. To add fractions, they need to have the same denominator, or same name. 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3. This means that the fractional part of the cookies that are peanut butter is 1 – 2/3 = 1/3. 1/3 of the cookies are peanut butter and 12 peanut butter cookies were baked. 12 is 1/3 of 36, so Becky baked a total of 36 cookies.
Middle School:
Question: A bicycle originally costs $250. The store is having a sale and offering a 20% discount on this item. What is the final price of the bicycle if there is a 7% sales tax?
Answer: $214
Solution: One way to solve this problem is to find the discounted price and then apply the sales tax. The bike originally costs $250 and there is a 20% discount. Percent means for each hundred. So, 20% of 250 is 20 + 20 + 10 = 50. So, the original price is discounted by $50. $250 – $50 = $200. The discounted price of the bicycle is $200. Now we apply the sales tax to the new price. 7% of 200 is 7 + 7 = 14. So, we add $14 for the sales tax. So, the final price for the bicycle is $214.
Algebra and Up:
Question: Determine where the lines 2y = 4x + 10 and 4x + 3y = 5 intersect.
Answer: (–1, 3)
Solution: Determining where two lines intersect is the same as solving a system of linear equations. One way to solve this problem is to use substitution.
2y = 4x + 10
4x + 3y = 5
Reduce the first equation by dividing both sides by 2.
y = 2x + 5
4x + 3y = 5
Substitute the first equation into the second equation.
4x + 3(2x + 5) = 5
Distribute the 3.
4x + 6x + 15 = 5
Simplify the left side by combining like terms.
10x + 15 = 5
Subtract 15 from both sides.
10x = –10
Divide by 10
x = –1
So, the x-coordinate is –1. To find the y-coordinate, we can substitute the x-value into either equation. Let’s substitute the x-value into the first equation.
y = 2(–1) + 5
Multiply.
y = –2 + 5
Simplify.
y = 3
The point where the two lines intersect is (–1, 3).
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