Tom and Jerry took a 10-minute Mathematics quiz. They started and ended the quiz at the same time, Tom answered 2 questions more than Jerry for every minute. Together, they answered 58 questions. How many questions
did Jerry answer?
Let's call the number of questions Jerry answered "J" and the number of questions Tom answered "T".
We know from the problem that:
- The quiz was 10 minutes long, so T = J + 2 for each minute.
- Together, they answered 58 questions, so T + J = 58.
We can use the first equation to substitute for T in the second equation:
(J + 2) + J = 58
Simplifying:
2J + 2 = 58
2J = 56
J = 28
So Jerry answered 28 questions.
To check, we can use the first equation to find Tom's number of questions:
T = J + 2 = 30
And indeed, 28 + 30 = 58.
Let's assume that Jerry answered x questions in total.
Since Tom answered 2 questions more than Jerry for every minute, Tom answered x + 2 questions for every minute.
Since they took a 10-minute quiz, Jerry answered x questions in 10 minutes, and Tom answered (x + 2) questions in 10 minutes.
Together, they answered a total of 58 questions, so we can set up the equation:
10x + 10(x + 2) = 58
Simplifying the equation:
10x + 10x + 20 = 58
20x + 20 = 58
Subtracting 20 from both sides:
20x = 58 - 20
20x = 38
Dividing both sides by 20:
x = 38 / 20
x = 1.9
Since we cannot have a fraction for the number of questions, we round down to the nearest whole number.
Therefore, Jerry answered 1 question in the quiz.
To solve this problem, we can use algebraic equations. Let's consider the number of minutes as M and assume that Tom answered X questions in each minute.
Since Tom answered 2 questions more than Jerry for every minute, Jerry must have answered X - 2 questions in each minute.
We know that the total number of questions they answered together is 58.
So, we can create the following equation:
Tom's total questions + Jerry's total questions = 58
In each minute, Tom answered X questions, and the number of minutes is M. Therefore, his total questions can be calculated as M * X.
In each minute, Jerry answered X - 2 questions, and the number of minutes is also M. Therefore, his total questions can be calculated as M * (X - 2).
Putting it all together, we have the equation:
M * X + M * (X - 2) = 58
Now, we need to solve this equation to find the values of M and X.