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Levart [38]
3 years ago
5

Three times a number added twice a smaller number is 4. Twice the smaller number less than twice the larger number is 6. Find th

e number
Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Answer:

x= -2/5 and y=13/5

Step-by-step explanation:

Lets assume that the larger number = x

And the smaller number = y

According to the given statement three times a number added twice a smaller number is 4, it means;

3x+2y=4 -------- equation 1

Now further twice the smaller number less than twice the larger number is 6,it means;

2y-2x=6 --------equation 2

Solve the equation 2.

2y=2x+6

y=2x+6/2

y=2(x+3)/2

y=x+3

Substitute the value of y=x+3 in the first equation.

3x+2y=4

3x+2(x+3)=4

3x+2x+6=4

Combine the like terms:

5x=4-6

5x=-2

x= -2/5

Put the value x= -2/5 in equation 2.

2y-2x=6

2y-2(-2/5)=6

2y+4/5=6

By taking L.C.M we get

10y+4/5=6

10y+4=6*5

10y+4=30

10y=30-4

10y=26

y=26/10

y=13/5

Hence x= -2/5 and y=13/5....

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Answer:

The differential equation for the amount of salt A(t) in the tank at a time  t > 0 is \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t

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It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

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