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Dafna11 [192]
3 years ago
8

Peter has money in two savings accounts. One rate is 6% and the other is 14%. If he has $900 more in the 14% account and the tot

al interest is $221, how much is invested in each savings account?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0

Answer:

  • $1375 at 14%
  • $475 at 6%

Step-by-step explanation:

Let x represent the amount Peter invested at 14%. Then (x-900) is the amount he invested at 6%. His total interest earned is ...

  0.14x + 0.06(x -900) = 221

  0.20x = 275 . . . . . . . . . . . . . . . . add 54, simplify

  x = 1375 . . . . . . . . . . . . . . . . . . . .divide by 0.2; amount invested at 14%

  (x-900) = 475 . . . . . . . . . . . . . . . amount invested at 6%

Peter invested $475 in the 6% account and $1375 in the 14% account.

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While mining, Nancy found a large metal bar that weighed 24 ounces, Nancy was also able to determine that the bar had 18 ounces
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Answer:

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2 years ago
The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars
stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = 253x-2x^2

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

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Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= 253x-2x^2 - (3x + 6972)

= 253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\

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We know that at break even point

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Hence P(x) = 0

-2x^2+250x-6972=0\\

now we have to solve the above equation for x

Dividing both sides by -2 we get

x^2-125x+3486=0

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

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Step-by-step explanation:

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How can you use negative numbers to represent real-world problems
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