el dinero de los demás. Si cada uno pierde una apuesta en el orden de presentación y al final terminan con
S/.48, S/.56 y S/.28 respectivamente, ¿Quién de los
amigos ganó más dinero y cuánto?
Answer:
La persona que ganó más dinero fue Braulio por S/.16
Step-by-step explanation:
Deje que la cantidad inicial sea Andrés X, Braulio Y y Ciro Z
Luego, dado que cada uno pierde una apuesta en el orden presentado, tenemos;
Después de la primera apuesta, tenemos;
Andrés X-Y-Z, Braulio (Y + Y), Ciro (Z + Z)
En la segunda apuesta, tenemos;
2 (X-Y-Z), 2Y - (X-Y-Z) - 2Z, 2Z + 2Z
2 (X-Y-Z), 3Y - X -Z, 4Z
En el tercero
4 (X-Y-Z), 6Y - 2X - 2Z, 4Z-2 (X-Y-Z) - (3Y - X -Z)
4 (X-Y-Z), 6Y - 2X - 2Z, 7Z - X - Y
4 (X-Y-Z) = 0.48 .............................. (1)
6Y - 2X - 2Z = 0.56 ...................... (2)
7Z - X - Y = 0.28 ............................ (3)
Multiplicamos las ecuaciones (2) por 2 y restamos la ecuación (1), tenemos;
12Y - 4X - 4Z - 4X + 4Y + 4Z = 0.56 * 2 - 0.48 = 0.64
16Y - 8X = 0.64 ...................... (4)
Multiplicamos las ecuaciones (2) por 7/2 y sumamos a la ecuación (3), tenemos;
21Y - 7X - 7Z + 7Z - X - Y = 7/2 * 0.56 + 0.28
20Y - 8X = 2.24 ...................... (5)
Restando la ecuación (4) de la ecuación (5) tenemos;
20Y - 8X - 16Y - 8X = 2.24 - 0.64 =
4Y = 1.6
Y = 1.6 / 4 = 0.4
De la ecuación (5), tenemos;
20Y - 8X = 20 * 0.4 - 8X = 2.24
8X = 8 - 2.24 = 5.76
X = 5,76 / 8 = 0,72
De la ecuación (3), tenemos;
7Z - X - Y = 7Z - 0.72 - 0.4 = 0.28
7Z = 1.4
Z = 1.4 / 7 = 0.2
Por lo tanto tienen inicialmente
X₁ = 0.72
Y₁ = 0.4
Z₁ = 0.2
Después de jugar tienen;
X₂ = 0.48
Y₂ = 0.56
Z₂ = 0.28
Los cambios son
Andrés 0.48 - 0.72 = -0.24
Braulio; 0.56 - 0.4 = 0.16
Ciro 0.28 - 0.2 = 0.08
La persona que ganó más dinero fue Braulio por S/.16
The farmer's market has a total of 98 tents. the ratio of food tents to retail tents is 9:5. a. Write a system of linear equations that represent this situation. b. How many food tents are at the market? c. How many retail tents are at the market?
Answer:
Let x represents the food tents and y represents the retail rents.
As per the given statement: The farmer's market has a total of 98 tents.
⇒ ......[1]
Also, it is given that the ratio of food tents to retails tents is 9 : 5.
⇒
By cross multiply, we have;
5x = 9y
Divide both sides by 5 we get;
Substitute this value x in equation [1] to solve for y;
Combine like terms;
Multiply both sides by we get;
Substitute the value of y= 35 in to solve for x;
(a)
System of linear equation that represents situation is:
(b)
As x represents the food tents.
Therefore, 63 food tents are at the market.
(c)
y= 35 retail tents are at the market.
And Then Simplify it!
50 points!
Step 1: Simplify both sides of the equation.
5(−3x−2)−(x−3)=−4(4x+5)+13
5(−3x−2)+−1(x−3)=−4(4x+5)+13(Distribute the Negative Sign)
5(−3x−2)+−1x+(−1)(−3)=−4(4x+5)+13
5(−3x−2)+−x+3=−4(4x+5)+13
(5)(−3x)+(5)(−2)+−x+3=(−4)(4x)+(−4)(5)+13(Distribute)
−15x+−10+−x+3=−16x+−20+13
(−15x+−x)+(−10+3)=(−16x)+(−20+13)(Combine Like Terms)
−16x+−7=−16x+−7
−16x−7=−16x−7
Step 2: Add 16x to both sides.
−16x−7+16x=−16x−7+16x
−7=−7
Step 3: Add 7 to both sides.
−7+7=−7+7
0=0
Answer:
All real numbers; the simplification is described below.
Step-by-step explanation:
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
Let's keep in mind PEMDAS (the order of operations) to simplify and solve this. First, we'll distribute inside each set of parenthesis!
5(-3x) + 5(-2) -1(x) -1(-3) = -4(4x) -4(5) + 13
See how we've taken the outer term on the outside of the parenthesis and multiplied it to each term inside the parenthesis. Simplify further.
-15x - 10 - x + 3 = -16x - 20 + 13
Now we can combine like terms! I will bold the terms I am combining.
-15x - 10 - x + 3 = -16x - 20 + 13 (combining the x terms on the left)
-16x - 10 + 3 = -16x - 20 + 13 (combining the constants on both sides)
-16x - 7 = -16x - 7
Aha! It looks like we have an equation that's literally equal to itself. If we were to simplify this, or put in any number, we'd get that number equals itself. For example:
-16(1) - 7 = -16(1) - 7
-16 - 7 = -16 - 7
-21 = -21
Any number you put in here will make the equation true, so these lines must be the same line. That means the solution is all real numbers.