Question

Sam, if you give me 5 pieces of candy from your bag, I'll have as many pieces as you. Sam laughed and answered, "No, you give me 5 of yours and I'll have twice as many as you."

a) Sam has 5 pieces of candy.
b) You have 10 pieces of candy.
c) Sam has 10 pieces of candy.
d) You have 5 pieces of candy.

Answer 1

By creating two equations from the given scenarios and solving them, we find that Sam has 35 pieces of candy and you have 25 pieces of candy.

Step-by-step explanation:

Let's denote the number of pieces of candy that Sam has as 'S' and the number that you have as 'Y'. We need to examine two scenarios based on the information provided.

Scenario 1: If you are given 5 pieces of candy from Sam, you would both have the same amount, so we can say that:

Y + 5 = S - 5

Scenario 2: If Sam is given 5 pieces of candy from you, then Sam would have twice as many pieces as you, which we can express as:

S + 5 = 2(Y - 5)

Combining both equations, we have:

• Y + 5 = S - 5
• S + 5 = 2(Y - 5)

By solving these two equations, we find that:

• Y + 10 = S
• S + 5 = 2Y - 10

Substitute Y + 10 for S in the second equation:

Y + 10 + 5 = 2Y - 10

Combine like terms:

Y + 15 = 2Y - 10

Now we isolate Y:

15 + 10 = 2Y - Y

Y = 25 pieces of candy for you

And since S = Y + 10:

S = 25 + 10

S = 35 pieces of candy for Sam

Therefore, the correct statements are that Sam has 35 pieces of candy and you have 25 pieces.