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Papessa [141]
3 years ago
9

Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they hav

e sold a total of 45 items and earned $195. If hot dogs cost $4 and hamburgers cost $5, how many did they sell of each?
What would be a system of equations for the scenario above?
Mathematics
1 answer:
diamong [38]3 years ago
3 0

Answer:

15 hamburgers were sold and 30 hotdogs were sold.

The systems of equations are x + y = 45 and 4x + 5y = 195.

Step-by-step explanation:

Let's make two equations.

x + y = 45

This represents the total of hotdogs and hamburgers sold

4x + 5y = 195

This represents the amount of money made for each food.

These are systems of equations, when you use 2 equations to solve a problem. I will use the strategy, Elimination for the following systems of equations. Anyways the goal is to multiply a number to x + y = 45 to cancel out one of the variables in 4x + 5y = 195. In other words, when we add these equations, the sum of the xs or ys will equal 0.

Let's multiply -5 to both x and y.

Now we have -5x -5y = -225 + 4x + 5y= 195

We will end up with -x = -30. This means that x = 30.

Now that we know x = 30, we can plug in 30 as x in one of the equations. I will plug in 30 into x + y = 45. 30 + y = 45.

Solve for y in 30 + y = 45, so y=15.

This means 15 hamburgers were sold and 30 hotdogs were sold.

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How can you write the expression with rationalized denominator? sqrt3 - sqrt6 / sqrt 3 + sqrt 6
harina [27]
Answer:  2√2 - 3

Explanation:


The expession written properly is:

\frac{ \sqrt{3}- \sqrt{6}  }{ \sqrt{3}+ \sqrt{6} }

To rationalize that kind of expressions, this is to eliminate the radicals on the denominator you use conjugate rationalization.

That is, you have to multiply both numerator and denominator times the conjugate of the denominator.

The conjugate of √3+√6 is √3 - √6, so let's do it:

\frac{ \sqrt{3} - \sqrt{6} }{ \sqrt{3} + \sqrt{6} } . \frac{ \sqrt{3}- \sqrt{6}  }{ \sqrt{3}- \sqrt{6} }

To help you with the solution of that expression, I will show each part.

1) Numerator: (√3 - √6) . (√3 - √6) = (√3 - √6)^2 = (√3)^2 - 2√3√6 + (√6)^2 =

= 3 - 2√18 + 6 = 9 - 6√2.

2) Denominator: (√3 + √6).(√3 - √6) = (√3)^2 - (√6)^2 = 3 - 6 = - 3

3) Then the resulting expression is:

 9 - 6√2
-----------
 -3

Which can be further simplified, dividing by - 3

    -3 + 2√2

Answer: 2√2 - 3

7 0
3 years ago
Read 2 more answers
Solve the equation. Round to the nearest tenth if necessary.
ASHA 777 [7]
The answer will be 30
5 0
3 years ago
Please this is your answer.​
Effectus [21]

Answer:

10. it is correct it is 24

11. 21

Step-by-step explanation:

I could not see the answer but it should look like this:

11.6-3(3-[2-3]-10)-3

6-3(3-[-1]-10)-3

6-3(3-(-1)-10)-3

6-3(4-10)-3

6-3(-6)-3

6-(-18)-3

(6-(-18))-3

24-3

21

4 0
2 years ago
Read 2 more answers
0.403 divided by 100 what is the quotient
Alja [10]

Answer: 0.403 / 100 = 0.00403


Hope this helps ♥️

4 0
1 year ago
4.5(8 - x) + 36 = 102 - 2.5(3x + 24)
Luden [163]

Answer:

x = -10

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   36 - 4.5x + 36 = 102 - 7.5x - 60
  2. Combine like terms:                   -4.5x + 72 = -7.5x + 42
  3. Add 7.5x on both sides:             3x + 72 = 42
  4. Subtract 72 on both sides:        3x = -30
  5. Divide 3 on both sides:              x = -10

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24)
  2. Simplify:                               4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24)
  3. Multiply:                               4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24)
  4. Add:                                     4.5(18) + 36 = 102 - 2.5(-6)
  5. Multiply:                               81 + 36 = 102 + 15
  6. Add:                                     117 = 117

Here we see that 117 does indeed equal to 117.

∴ x = -10 is a solution of the equation.

7 0
3 years ago
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