The ratio of rock music to total discs that Ellen owns is 25/40. Paul has 50 rock music discs. The ratio of rock music to total discs in his collection is equivalent to the ratio of rock music to total discs in Ellen's collection. how many discs do they own?
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I didn't understand what the T meant so like I couldn't figure out the question because it wasn't specific enough for me to understand
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To solve this problem, we can set up a proportion based on the given information. Let's call the total number of discs Paul owns as "P" and the total number of discs Ellen owns as "E."
Based on the information given, we know that the ratio of rock music to total discs for Ellen is 25/40, which simplifies to 5/8.
We also know that Paul has 50 rock music discs. Let's call the total number of discs in his collection "T." Therefore, the ratio of rock music to total discs for Paul is 50/T.
Now, we can set up the proportion:
5/8 = 50/T
To find the value of T, we can cross-multiply:
5T = 8 * 50
5T = 400
T = 400/5
T = 80
So, Paul owns a total of 80 discs.
To find the total number of discs Ellen owns, we can substitute the value of T into the original ratio for Ellen:
25/40 = rock music discs (which is 5/8) / total discs for Ellen
25/40 = (5/8) / E
To solve for E, we can cross-multiply:
25 * E = 40 * 5/8
25E = 200/8
25E = 25
E = 25/25
E = 1
Therefore, Ellen owns a total of 1 disc.
In conclusion, Paul owns 80 discs and Ellen owns 1 disc.
120
25/40 = 50/T
Solve for T.
T + 40 = ?