We have 2 types of tickets, A tickets and B tickets. The total number of tickets sold was 500, so an equation for this NUMBER of tickets is A + B = 500. The MONEY equation is something different. A tickets cost 10, so they are represented by 10A; B tickets cost 60, so they are represented by 60B. The total dollar sales for A and B are 6000. Our money equation for the sales is 10A + 60B = 6000. Solve the first equation for A: A = 500 - B. Sub that value for A into the second equation to solve for B: 10(500-B) + 60B = 6000. Distribute through the parenthesis to get 5000 - 10B + 60B = 6000. Combine like terms to get 50B = 1000. B = 20. There were 20 type B tickets sold. A = 500 - B, so A = 500 - 20 and A = 480. There were 480 type A tickets sold.

3 0

4 years ago

Solve for u<br> -1/5 + 1/2 u = -2/3

Tju [1.3M]

-1/5 + 1/2 u = -2/3
-6/30 + 15/30 u = -20/30
+6/30 +6/60
___________________
15/30 u = -14/30
(15/30 u = -14/30) ÷ (15/30)
u = -14/15
u = -.933

3 0

3 years ago

Solve each equation 3x^2=80

Lapatulllka [165]

Answer:

$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

$x = \frac{\pm4\sqrt{15}}{3}$

Step-by-step explanation:

Hello!

Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

First, let's convert our equation to standard form of a Quadratic: ax² + bx + c = 0

3x² = 80

3x² - 80 = 0

Note, thats the value of b will be 0, as there is no "bx"

Now, solve:

$x = \frac{-(0) \pm \sqrt{(0)^2 - 4(3)(-80)}}{2(3)}$ Plug in values
$x = \frac{\pm\sqrt{960}}{6}$ Simplify the radical (Discriminant)
$x = \frac{\pm8\sqrt{15}}{6}$ Pull out perfect squares
$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$ Reduce factors

The solutions are $x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

5 0

3 years ago

A house is 25 feet tall and a ladder is set up 35 feet away from the side of the house. approximately how long is the ladder fro

maks197457 [2]

Use Pythagorean Theorem of a^2 + b^2 = c^2 where a and b are the legs of the triangle set up by the house height and the ground, and c is the hypotenuse or how long the ladder is. C is going to be our unknown.

Just plugging in you get 25^2 + 35^2 = c^2. Simplify to 625 + 1225 = c^2. Simplify again to 1850 = c^2. The square root both sides to isolate the variable c. C = sqrt(1850) or approximately 43.0116 feet if rounded to 4 decimal places.

The ladder is approximately 43.0116 feet long.

4 0

3 years ago