Story Problem
Some friends are recording songs on a CD. The first 1/5 of the CD has Alex's songs.The next 12 minutes of songs are Henrique's. 1/3 of the time is Brian's songs. Sally has 32 minuites. How many minutes of music are there in all?
If we add up everybody's time, we should get the total time of the CD.
Let M represent the total time of the CD. Everything will be in minutes.
M= (1/5)*M + 12 + (1/3)*M + 32
Combining terms...
(1 - 1/5 - 1/3)*M=44
Solve for M
Thank you. We came up with 94 2/7 which is approximately 94mins, 17 secs.
Good!
That is what I got, also.
the quotient of eight and twice a number
I need help withrational numbers
To find the total number of minutes of music on the CD, we need to add up the minutes for each friend's songs.
Step 1: Determine the minutes of Alex's songs.
The first 1/5 of the CD is Alex's songs. Since we don't know the total duration of the CD, we'll use a variable, let's say "x," to represent the total minutes. So, Alex's songs would be (1/5)*x minutes.
Step 2: Determine the minutes of Henrique's songs.
The next 12 minutes are Henrique's songs.
Step 3: Determine the minutes of Brian's songs.
1/3 of the time on the CD is Brian's songs. So, Brian's songs would be (1/3)*x minutes.
Step 4: Determine the minutes of Sally's songs.
We know Sally has 32 minutes of music.
Now, we can add up all the minutes to find the total duration of the CD:
Alex's songs + Henrique's songs + Brian's songs + Sally's songs = Total duration of the CD
[(1/5)*x] + 12 + [(1/3)*x] + 32 = Total duration of the CD
Now, let's solve for x:
(1/5)*x + 12 + (1/3)*x + 32 = x
Multiply through by 15 to get rid of the fractions:
3x + 180 + 5x + 480 = 15x
8x + 660 = 15x
660 = 15x - 8x
660 = 7x
Divide by 7 to solve for x:
x = 660/7
x ≈ 94.29
So the total duration of the CD is approximately 94.29 minutes.