Question

A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amounts of money he may have after he sees Rita?

A. |x – 42.80| = 12
B. |x + 42.80| = 12
C. |x – 12| = 42.80
D. |x + 12| = 42.80

Answer 1

A. |x – 42.80| = 12

Explanation:

Given,

The initial amount in Jame's wallet = $ 42.80,

Let x represents the final amount in Jame's wallet after seeing Rita,

According to the question,

Either he will borrow $ 12 from Rita or Rita will borrow $ 12 from him,

When he borrows $ 12 from Rita,

Final amount in the wallet = initial amount + borrowed amount

⇒ x = 42.80 + 12

⇒ x - 42.80 = 12 ------(1)

While, when Rita borrows $ 12 from him,

Final amount in the wallet = initial amount - borrowed amount

⇒ x = 42.80 - 12

⇒ x - 42.80 = -12

⇒ -(x - 42.80) = 12 -------(2),

By combining equation (1) and (2),

We get,

| x-42.80 | = 12

Which is the required equation.

⇒ Option A is correct.

Answer 2

First option is correct.

Explanation:

Let amounts of money James may have after he sees Rita be x.

It is given that either James borrowed $12 from his friend Rita or she borrowed $12 from him.

So meeting Rita second time either he will $12 or he will receive $12.

The amounts of money James may have after second meeting with Rita is:

Case 1: If he pays $12.

`x=42.80-12` .... (1)

Case 1: If he receives $12.

`x=42.80+12` .... (2)

On combining equation (1) and (2), we get

`x=42.80\pm 12`

Subtract 42.80 from both sides.

`x-42.80=\pm 12`

It can be written as

`|x-42.80|=12`

Therefore first option is correct.