Lower Elementary
Question: Todd, Jeremy, and Miranda went out trick or treating on Halloween. Todd and Jeremy both came back with 2 pounds of candy each and Miranda returned with 5 pounds of candy. If they decide to put all of their candy together and divide it up equally, how many pounds of candy do each of them get?
Answer: 3 pounds of candy each
Note: Because they combined all their candy we add how much candy each person has together with the others.
2 pounds + 2 pounds + 5 pounds = 9 pounds
Together they have 9 pounds of candy and they want to split it equally between themselves. Because 9 pounds can be broken into 3 equal groups of 3 pounds, each person gets 3 pounds of candy.
Upper Elementary
Question: This Halloween Kisha wants to make sure that she has enough candy for all the trick or treaters that will come to her house. In each bag of candy that she buys from the store are 100 pieces of candy. If she wants to give each trick or treater 3 pieces of candy and she is preparing for 125 trick or treaters, how many bags of candy should she buy?
Answer: 4 bags
Note: Kisha is preparing for 125 trick or treaters and every trick or treater will get 3 pieces of candy. Altogether Kisha will need 375 pieces of candy (125 x 3 = 375). Each bag of candy has 100 pieces of candy so Kisha will need 4 bags of candy.
Middle School
Question: Lauren bought 3 pumpkins; a large pumpkin, a small pumpkin, and an average pumpkin. The large pumpkin was twice the weight of the small pumpkin and the small pumpkin was 2/3 the weight of the average pumpkin. If the average pumpkin weighs 15 pounds, how much does the large pumpkin weigh?
Answer: 20 pounds
Note: Because we know the weight of the average pumpkin to be 15 pounds, let’s start there and work backwards. The small pumpkin is 2/3 the weight of the average pumpkin.
1/3 of 15 pounds is 5 pounds, so 2/3 of 15 would be 10 pounds (5 pounds + 5 pounds).
The large pumpkin is twice the weight of the small pumpkin. Because the small pumpkin is 10 pounds, the large pumpkin would be 20 pounds (2 x 10 pounds).
Algebra and Up
Question: David, Wes, and Jaime went trick or treating on Halloween. Altogether, the three of them collected 57 pieces of candy. Wes collected four more than three times the number of pieces of candy collected by David. Jaime collected seven less than the number of pieces of candy collected by Wes. How much candy did each of them collect?
Answer: David = 8, Wes = 28, and Jaime = 21
Note: This problem give us 3 unknown variables, d, w, and j which represent how much pieces of candy David, Wes, and Jaime have respectively. In order to solve for the 3 unknown variables we will need to write 3 equations.
d + w + j = 57 (1)
w = 4 + 3d (2)
j = w – 7 (3)
There are multiple ways of solving this system of equations, but we will do it by solving for w and d in terms of j for equations 2 and 3 and plugging them into the equation 1.
Solving for w in equation 1:
j = w – 7
w = j + 7 (4)
Plugging in “j + 7” into w for equation 2 and solving for d.
j + 7 = 4 + 3d
d = 1/3 â— (j + 3) (5)
Plugging equations 4 and 5 into equation 1 allows us to solve for j.
d + w + j = 57
1/3 â— (j + 3) + j + 7 + j = 57
Multiply everything by 3 to get rid of the fraction.
j + 3 + 3j +21 +3j = 171
Combined like terms and solve for j.
7j + 24 = 171
7j = 147
j = 21
Now that we know j, we can go back and plug it in for equations 4 and 5 to solve for w and d.
w = j + 7 = 21 +7 = 28
d = 1/3 â— (j +3) = 1/3 â— (21 + 3) = 1/3 â— 24 = 8
