The problem statement gives a relation between the amount removed from one bag and the amount removed from the other. It asks for the amount remaining in each bag. Thus, there are several choices for variables in this problem, some choices resulting in more complicated equations than others.
Let's do it this way: let x represent the amount remaining in bag 1. Then the amount removed from bag 1 is (100-x). The amount remaining in bag 2 is 2x, so the amount removed from that bag is (100-2x). The problem statement tells us the relationship between amounts removed:
... (100 -x) = 3(100 -2x)
... 100 -x -3(100 -2x) = 0 . . . . . . subtract the right side
... 5x -200 = 0 . . . . . . . . . . . . . . eliminate parentheses and collect terms
... x -40 = 0 . . . . . . . . . . . . . . . . .divide by 5
... x = 40 . . . . . . . . . . . . . . . . . . . add 40
- 40 kg is left in the first bag
- 80 kg is left in the second bag
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<u>Check</u>
The amount removed from the first bag is 60 kg. The amount removed from the second is 20 kg. The amount removed from the first bag is 3 times the amount removed from the second bag, as described.
Answer:
x = 4.5, 4/7
Step-by-step explanation:
To find the roots of a factored equation you need to set the y value at 0, that way you can solve for x. Once you solve for x you get two quantities, which can be graphed. These two quantities are where the x intercepts are.
Answer:
282 Hours after 6 weeks
Step-by-step explanation:
Multiply the 6 weeks and the 48 hour a week adverage and theres your answer!
Answer:
B. $3525.43
Step-by-step explanation:
We will use continuously compound interest formula to solve our problem.
A= Amount after T years.
P= Principal amount.
r= Interest rate (in decimal form).
e= The mathematical constant e.
T= Time in years.
First of all we will convert our interest rate in decimal form.
Now let us substitute our given values in above formula.
Therefore, we will get an amount of $3525.43 after 10 years and option B is the correct choice.
Answer: 6
Step-by-step explanation:
From the question, we are informed that a band expects to put 15 songs on their next CD and that the band writes and records 60% more songs than they expect to put on the CD. Therefore, the total songs will be:
= 15 + (60% × 15)
= 15 + (0.6 × 15)
= 15 + 9
= 24 songs.
During the editing process, 75% of the songs are removed. The total number of songs that will be there on the final CD will be:
= 24 - (75% × 24)
= 24 - (0.75 × 24)
= 24 - 18
= 6
6 songs will be there on the final CD.
