Question

Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.

Let x = the number of games played.


Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?


A. The variable x should represent the amount of money left.

B. From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.

C. The equation should have sums on both sides.

D. From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.

Answer 1

Answer: Option B

From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.

Explanation:

To solve this problem, let's consider the initial equation that Jorge had.

`8.25-0.25x=9.75-0.75x`

Subtract 9.75 on both sides of equality

`8.25-9.75-0.25x=9.75-9.75-0.75x`

`-1.50-0.25x=-0.75x`

Add 0.25x on both sides of equality

`-1.50-0.25x+0.25x=-0.75x+0.25x`

`-1.50=-0.50x`

`x=3`

You can see then that Jorge's error was adding
`-0.75x + 0.25x`

When this sum is correctly done, the result is
`-0.50x`

The answer is the option B.

Answer 2

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Explanation:

If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by: 8.25 - 0.25X.

If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by: 9.75 - 0.75X.

If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:

Equation: 8.25 - 0.25X = 9.75 - 0.75X

Step 1: -1.50 - 0.25X = - 0.75X

Step 2: -1.50 = - 0.50X

Step 3: x=3

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.