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lesya [120]
3 years ago
11

A contest gives out prizes for first, second, and third place. First place is $500 more than double third place. Second place is

$400 less than first place. All together, $1850 is given out in prizes. How much is each prize worth?
Mathematics
1 answer:
topjm [15]3 years ago
5 0

9514 1404 393

Answer:

  1. $1000
  2. $600
  3. $250

Step-by-step explanation:

Let t represent the third-place prize value. Then the first place prize has a value of 2t+500, and the second-place prize is 2t+100. The total value of the three prizes is ...

  t +(2t+500) +(2t+100) = 1850

  5t +600 = 1850

  5t = 1250

  t = 250 . . . . . . . . . . . third place prize

  2t +500 = 1000 . . . . first place prize

  1000 -400 = 600 . . .second place prize

The prizes for 1st, 2nd, and 3rd places are $1000, $600, and $250, respectively.

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Rex puts $5,000 in a savings account with a simple
Mashcka [7]

Answer:

Rex earns $250 in interest after 2 years.

Step-by-step explanation:

5 0
3 years ago
Keith won a cash prize in an art competition. He gave his mother 2/5 of the money he won. Of the remainder, 1/4 was given to his
USPshnik [31]

Answer:

300 dollars

Step-by-step explanation:

Let the original amount = x

x - 2/5x  was what his mother's share looked.

5/5 x - 2/5 x

3/5x is what is left.

3/5 x - 1/4 * 3/5 x - 2/3x * 3/5 = his sister's share and his brothers

3/5x - 1/4*3/5 x - 2/3 * 3/5 = 15

3/5x * (1 - 1/4 - 2/3) = 15

3/5 x 5/60 = 15

15 / 300 * x = 15

1/20  x = 15

x = 15 * 20

x = 300

7 0
3 years ago
Whats the difference between linear equations and quadratic equation
SIZIF [17.4K]

Answer:

Step-by-step explanation:

A linear equation in two variables doesn't involve any power higher than one for either variable. It has the general form Ax + By + C = 0, where A, B and C are constants. ... A quadratic equation, on the other hand, involves one of the variables raised to the second power. It has the general form y = ax2 + bx + c

4 0
3 years ago
Determine whether the point (2, 2) is a solution to the system of equations. Explain your reasoning in complete sentences. Prove
goblinko [34]

Answer:

(0,2) is the solution of the given functions.

Step-by-step explanation:

We have been given two functions  f(x)=|x-1|+1  and g(x)=3x+2

To find the solution of the two functions mathematically, we will equate the given functions:

3x+2=|x-1|+1

3x+1=|x-1|

When we will open the modulus function we will have two values +, -

In positive case:

3x+1 =x-1

2x=-2

x=-1

Now, substitute x=-1 in g(x)=3x+2 we get

g(-1)=3(-1)+2=-1

Hence, (-1,-1) is the solution of the given functions.

In negative case:

Now, 3x+1=-(x-1)

3x+1=-x+1

4x=0

x=0

Now, put x=0 in g(x)=3x+2 we get

g(0)=3(0)+2=2

We have another solution: (0,2)

The point (2,2) is not the solution.

And graphically, the solution of two functions is their intersection point which is (0,2)

Hence, (0,2) is the solution of the function.


6 0
3 years ago
The table shows the number of points Malik and Alexia scored while playing a video game together.
grigory [225]

Answer:

a=m+30

Step-by-step explanation:

because you see that malik is always 30 points under, and A would be Alexia and M is Malik,

                                        The answer is a=m+30

5 0
3 years ago
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