Problems of the Week: September 14 - 18

Sep 22, 2020 | North Alpharetta

Lower Elementary:

Question: Natalie prepares 16 ounces of broccoli for family dinner night. Each of the 4 people in Natalie’s family eat the same amount of broccoli, and there are 4 ounces of broccoli left over. How many ounces of broccoli does each family member eat?

Answer:  3 ounces

Solution:  First, we subtract the leftover broccoli; 16 ounces – 4 ounces = 12 ounces of broccoli are eaten by Natalie’s family. Since each family member eats the same amount, we divide 12 ounces into 4 equal groups and get 3 ounces in each. So, each family member eats 3 ounces of broccoli.

Upper Elementary:

Question: William used to drink 6 cans of soda per day, but he decided to replace his soda with bottled water. If a can of soda costs $0.85 and a bottle of water costs $0.75, then how much money does William save each week by swapping from soda to water?

Answer:  $4.20

Solution:  Each soda costs $0.10 more than a bottle of water. So, each day, William saves $0.10 × 6 = $0.60. In a week, he saves $0.60 × 7 = $4.20.

Middle School:

QuestionA 12-ounce steak has 92 grams of protein. A 6-ounce serving of chicken has 52 grams of protein. A 9-ounce serving of salmon has 63 grams of protein. If Mason wants to cook the option with the most protein per ounce, then which should he choose?

Answer:  Chicken

Solution:  If we divide the grams of protein in each option by the weight of the serving of meat, then we can compare the amounts of protein per ounce. There are 92 ÷ 12 = 72/3 grams of protein per ounce in the steak, 52 ÷ 6 = 82/3 grams of protein per ounce in the chicken, and 63 ÷ 9 = 7 grams of protein per ounce in the salmon. So, the chicken has the most protein per ounce.

Algebra and Up:

Question: A 16–ounce green smoothie with 1 scoop of super vitamin powder costs $4.85. A 16–ounce green smoothie with 3 scoops of super vitamin powder costs $5.55. Write a function of x, the number of scoops of super vitamin powder, that yields the cost of a green smoothie.

Answer:   f(x) = $0.35x + $4.50

Solution:  First, we notice that when the number of scoops of super vitamin powder increases by 2, the price increases by $5.55 – $4.85 = $0.70. So, each scoop of super vitamin powder costs $0.35. To find the cost of a 16–ounce smoothie without the super vitamin powder, we can subtract $4.85 – $0.35 = $4.50. So, the cost of a green smoothie is $4.50 plus the total of $0.35 times the number of scoops:

f(x) = $0.35x + $4.50