Question

Anshu gave Bobby and Chandana as many pens as each one of them already had. Then Chandana gave Anshu and Bobby as many pens as each already had Now each had an equal number of pens. The total number of pens is 72.​

Answer 1

To solve this problem, first assign variables to represent the number of pens each person has. Then create equations based on the information given, such as Anshu giving pens to Bobby and Chandana and Chandana giving pens back to Anshu and Bobby. Finally, solve the equations to find the number of pens each person had. So, Bobby had 12 pens, Chandana had 48 pens, and Anshu had 24 pens.

Step-by-step explanation:

Let's assign variables to represent the number of pens each person already has. Let's say Bobby has x pens, Chandana has y pens, and Anshu has z pens.

Anshu gives Bobby and Chandana x pens each, so Bobby now has x + x = 2x pens, and Chandana has y + x pens.

Chandana gives Anshu and Bobby y pens each, so Anshu now has z + y pens, and Bobby has 2x + y pens.

Now, we know that they each have an equal number of pens, so 2x + y = z + y.

The total number of pens is 72, so 2x + y + z = 72.

From the equation 2x + y = z + y, we can simplify it to 2x = z.

Substituting this into the equation 2x + y + z = 72, we get 2x + y + 2x = 72 or 4x + y = 72.

Now, we have two equations: 2x = z and 4x + y = 72.

Using trial and error, we can find that x = 12, y = 48, and z = 24. So, Bobby had 12 pens, Chandana had 48 pens, and Anshu had 24 pens.

Answer 2

To solve the pen distribution problem, we set up equations based on the given actions and the total pens. We discover that Anshu, Bobby, and Chandana must have started with 36, 18, and 18 pens, respectively, to end up with an equal number of pens totaling 72.

Step-by-step explanation:

Solving the Pen Distribution Problem

Let's assume Anshu started with A pens, Bobby with B pens, and Chandana with C pens. Anshu gave Bobby and Chandana as many pens as they had, so now Anshu has A - B - C pens, Bobby has 2B, and Chandana has 2C. Then Chandana gave Anshu and Bobby as many pens as they had, resulting in Anshu having 2A - 2B - 2C, Bobby having 2B + C, and Chandana having C pens. Each person now has an equal number of pens, meaning 2A - 2B - 2C = 2B + C = C. If we sum all the pens, we get 2A - 2B - 2C + 2B + C + C = 72. Simplifying, we find that 2A = 72, so Anshu must have started with 36 pens, Bobby with 18, and Chandana with 18 pens.