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.
Equation: 8.25 minus 0.25 x = 9.75 minus 0.75 x. Step 1: negative 1.50 minus 0.25 x = negative 0.75 x. Step 2: negative 1.50 = 0.50 x. Step 3: negative 3 = x.
Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?
The variable x should represent the amount of money left.
From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
The equation should have sums on both sides.
From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.
From Step 2 to Step 3, Jorge made a calculation error and divided both sides by the wrong number. He should have divided both sides by 0.50 instead of 0.50x. The correct step would be: x = -3/-0.50, which simplifies to x = 6. Therefore, after 6 games, Marcel and Floyd will have the same amount of money remaining.
After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave Susan 36 rocks, which equation could be used to determine how many rocks George started with?
One-half x = 36 + 5
One-half (x minus 5) = 36
One-half (x + 5) = 36
One-half x + 5 = 36
One-half x + 5 = 36 is the equation that could be used to determine how many rocks George started with.
If after getting 5 new rocks, George gave half of his rock collection (x/2) to Susan, then the equation would be:
x/2 + 5 = 36
Solving for x:
x/2 = 31
Multiplying both sides by 2:
x = 62
Therefore, George started with 62 rocks before giving half of his collection to Susan.
Jorge's error is in Step 1. He incorrectly subtracted 0.25x from both sides of the equation. The correct step would be to subtract 0.25x from ONLY the left side of the equation. The equation should be:
8.25 - 0.25x = 9.75 - 0.75x
By subtracting 0.25x only from the left side, the equation would become:
-1.50 = 0.50x
Then by dividing both sides by 0.50, the equation would be simplified to:
-3 = x
Jorge incorrectly skipped this division step, resulting in a negative x which does not make sense in the context of the problem.