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erik [133]
3 years ago
11

In a paint factory, an old conveyer line has filled 40 barrels of paint, and is filling more at a rate of 10 barrels per minute.

A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How long will that take? How many barrels will each line have filled?
Mathematics
2 answers:
zhenek [66]3 years ago
6 0

Answer:

20 minutes; 240 barrels

Step-by-step explanation:

Old line = 40 + 10t

New line = 12t

Equal when,

40 + 10t = 12t

40 = 2t

t = 20 minutes

Each line will have:

12t = 12(20) = 240 barrels

Evgen [1.6K]3 years ago
3 0

Answer:

20 minutes, 240 barrels

Step-by-step explanation:

Old line:   b(x) = 40 + 10x, where x is the number of minutes elapsed.

New line:  b2(x) = 12x

Equating these two functions results in

40 + 10x = 12 x, which, when simplified, comes out to

40 = 2x, or x = 20.

An equal number of barrels will have been filled after 20 minutes.

That number is b2(20) = 12(20) = 240, or 240 barrels.

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Answer:

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Step-by-step explanation:

<u>Solving Equations</u>

We have the expression:

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3 years ago
Dalia saved $3000 last year. She said $600 in the month of January. What percent of the total amount of money she saved last yea
Anni [7]
1. We assume, that the number 3000 is 100% - because it's the output value of the task. 
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 100% equals 3000, so we can write it down as 100%=3000. </span>
<span>4. We know, that x% equals 600 of the output value, so we can write it down as x%=600. </span>
5. Now we have two simple equations:
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2) x%=600
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=3000/600
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 600 is what percent of 3000

100%/x%=3000/600
<span>(100/x)*x=(3000/600)*x       - </span>we multiply both sides of the equation by x
<span>100=5*x       - </span>we divide both sides of the equation by (5) to get x
<span>100/5=x </span>
<span>20=x </span>
<span>x=20
So 600 is 20% of 3000</span>
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