A test of 60 minutes contains questions on mathematics and english only. the time taken to solve a mathematics question is twice the time taken to answer an english question and the ratio of time taken to solve all mathematics questions to time taken to answer all english questions is 8/7.
If the total number of question is 22, how many english questions can be aanswered in 18 minutes?
Please help me with this.
If there are m math questions which take 2x minutes each,
and e english questions which take x minutes each,
2xm + xe = 60
2xm/xe = 8/7
14xm = 8xe
7xm=4xe
7m=4e
m+e = 22
x(2m+e) = 60
x(8m+4e) = 240
x(15m) = 240
xm = 16
2xm + xe = 60
32 + xe = 60
xe = 28
xm+xe = 22x
16+28 = 22x
44=22x
x=2
So, english questions take 2 minutes each to answer.
The above equations were just as they occurred to me. They can probably be rearranged in a more coherent format.
Bad
You had to substitute x as 18 minutes and find e.
Well, it seems like you have quite the puzzling problem on your hands! Let's see if we can solve it with a touch of humor.
First, let's assume that the time taken to answer an English question is "x" minutes. That means the time taken to solve a Math question would be twice that, which is "2x" minutes.
According to the ratio given, the time taken to solve all Math questions to answer all English questions is 8:7. So, the total time for Math questions would be 8x minutes, and the total time for English questions would be 7x minutes.
Now, we know that the total number of questions is 22. So, we can set up an equation:
8x + 7x = 60
Combining like terms, we have:
15x = 60
Dividing both sides by 15, we find:
x = 4
So, the time taken to answer an English question is 4 minutes.
Now we can answer how many English questions can be answered in 18 minutes. Well, if it takes 4 minutes to answer one English question, then in 18 minutes you can answer:
18 minutes / 4 minutes per question = 4.5 English questions
Hmm, that's quite an interesting answer. You can't answer half a question, so the closest whole number is 4 English questions. I guess you can say time flies when you're having fun with English questions!
I hope this funny yet informative explanation helps you out!
To solve this problem, we can use a system of equations. Let's denote the time taken to solve an English question as 'e', and the time taken to solve a mathematics question as 'm'.
From the given information:
1) The time taken to solve a mathematics question is twice the time taken to answer an English question: m = 2e.
2) The ratio of time taken to solve all mathematics questions to time taken to answer all English questions is 8/7: (m * number of mathematics questions) / (e * number of English questions) = 8/7.
We know that the total number of questions is 22. Let 'n' be the number of mathematics questions and 'k' be the number of English questions. So, n + k = 22.
Now we can set up the equations and solve for 'k', the number of English questions that can be answered in 18 minutes.
First, substitute m = 2e into the ratio equation, we get:
(2e * n) / (e * k) = 8/7
(2n) / k = 8/7
Rearrange the equation:
14n = 8k
7n = 4k
We also know that n + k = 22, so we can substitute the second equation into the first equation:
7(22 - k) = 4k
154 - 7k = 4k
154 = 11k
k = 154 / 11
k = 14
Therefore, there are 14 English questions in the test. Now, we need to determine how many of these can be answered in 18 minutes.
Since the total test time is 60 minutes and the time taken to answer each English question is 'e', we can set up the equation:
14e = 60
e = 60 / 14
Now, we need to find how many e's can fit into 18 minutes:
18 / e = 18 / (60 / 14) = 18 * (14 / 60) = 4.2
Rounding down to the nearest whole number, we find that approximately 4 English questions can be answered in 18 minutes.