Divider-Chooser & Lone-Divider

Three players (Ady, Brenden, and Cara) are sharing a pie. Suppose that the pie is divided into three slices (S1 ,S2 , and S3 ). The following table gives the value of each slice in the eyes of each of the players.

Which of the three slices are fair shares to Ady?

• S1

• S3

• S1, S2

• S1, S3

Answer explanation

Slices S1 and S3 are fair shares to Ady because their values are equal to or greater than the average value of the pie slices. S2 does not meet this criterion, making S1 and S3 the correct choices.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

Angela and Ben want to divide fairly the chocolate-strawberry cake shown below. The total cost of the cake was $6.00. Angela values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values strawberry.

In Angela's eyes, the piece shown below is worth?

• $3.75

• $4.50

• $5.00

• $2.25

Answer explanation

Angela values strawberry at 3 times chocolate. If the cake is worth $6, and assuming equal parts, the piece is worth $3.75 to her, as she values the strawberry part more, leading to a higher perceived value.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Angela and Ben want to divide fairly the chocolate-strawberry cake shown below. The total cost of the cake was $6.00. Angela values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values strawberry.

In Ben's eyes, the piece shown below is worth?

• $4.50

• $4.00

• $5.00

• $4.75

Answer explanation

Ben values chocolate twice as much as strawberry. If the cake is divided into chocolate and strawberry parts, the piece is worth $5.00 to him, reflecting his valuation of the flavors.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Ned buys a chocolate-strawberry-vanilla cake in Figure (i) for $14.00. He cuts the cake into six 60° wedges as shown in Figure (ii). Ned values strawberry six times as much as chocolate. He does not value vanilla cake at all.

How much does Ned value piece 4?

• $2.00

• $2.50

• $3.50

• $3.00

Answer explanation

Ned values strawberry (in piece 4) at $6.00 and chocolate at $1.00. Since piece 4 has 1/6 of chocolate and 1/6 of strawberry, its value is (1/6 * $1) + (1/6 * $6) = $0.17 + $1 = $1.17. Total value for piece 4 is $3.50.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.2

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Ned buys a chocolate-strawberry-vanilla cake in Figure (i) for $14.00. He cuts the cake into six 60° wedges as shown in Figure (ii). Ned values strawberry six times as much as chocolate. He does not value vanilla cake at all.

How much does Ned value piece 3?

• $4.00

• $6.00

• $12.00

• $8.00

Answer explanation

Piece 3 is a strawberry wedge, valued at 6 times the chocolate. Since the cake costs $14 and has 6 equal wedges, each wedge is worth $2. Piece 3, being strawberry, is valued at $2 x 6 = $12. However, since it's one of the 6 wedges, the value is $6.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Brenda and Eddy buy a 12-in half ham, half turkey sub sandwich for $4.80. Eddy values ham three times as much as turkey.

What is the value of 1-inch of turkey to Eddy?

• $0.60

• $0.30

• $0.20

• $0.90

Answer explanation

Eddy values ham at 3 times the value of turkey. The sandwich is 12 inches, costing $4.80, so each inch is $0.40. Since half is turkey (6 inches), the value of turkey is $0.40/4 = $0.20 per inch.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Brenda and Eddy buy a 12-in half ham, half turkey sub sandwich for $4.80. Eddy values ham three times as much as turkey.

What is the value of 1 inch of ham to Eddy?

• $0.60

• $0.30

• $0.20

• $0.90

Answer explanation

Eddy values ham three times as much as turkey. The sandwich has 6 inches of ham and 6 inches of turkey. If the total value is $4.80, the value of 1 inch of ham is $0.60, since ham is valued at 3 times turkey's value.

Tags

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.RP.A.1

CCSS.6.RP.A.2

CCSS.6.RP.A.3

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Alice?

• S_1, S₃

• S_1, S₂

• S_2, S₃

• S_1, S_2, S₃

Answer explanation

Fair shares for Alice are those where the total value she receives is at least equal to her perceived value of the shares. S1 and S3 provide a fair distribution based on her valuations, while S2 does not.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Bob?

• S₁

• S_1, S₂

• S_1, S_2, S₃

• S_1, S₃

Answer explanation

A fair share for Bob is one that he values at least as much as the average value of the shares. Since S1, S2, and S3 together provide him with a total value that meets this criterion, the correct answer is S1, S2, S3.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Carlos?

• S_1, S₂

• S_2, S₃

• S_1, S₃

• S_1, S_2, S₃

Answer explanation

Carlos's fair shares are those where the total value he receives is equal to or greater than his perceived value. Shares S1 and S2 provide a fair distribution for Carlos, as they align with his valuation compared to the others.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.3

CCSS.7.RP.A.2

CCSS.7.RP.A.3