8 km Radius: Diameter: Area:

a charitable organization in Lanberry is hosting a black tie benefit. Yesterday, the organization sold 55 regular tickets and 49

jenyasd209 [6]

Answer:

regular: $67
VIP: $122

Step-by-step explanation:

Let r and v represent the costs of a regular and VIP ticket, respectively. The two sales can be represented by ...

55r +49v = 9663

79r +84v = 15541

We can subtract 7 times the second equation from 12 times the first to eliminate the v terms.

12(55r +49v) -7(79r +84v) = 12(9663) -7(15541)

660r +588v -553r -588v = 115,956 -108,787 . . . . . eliminate parentheses

107r = 7169 . . . . . . . simplify

r = 67 . . . . . . . . . . . divide by 107

Using this value in the first equation, we have ...

55(67) +49v = 9663

v = 5978/49 . . . . . . . . . subtract 3685, divide by 49

v = 122

A regular ticket costs $67; a VIP ticket costs $122.

_____

Additional comment

When using "elimination" to solve a system of equations, you're looking for coefficients of the same variable that are related by small factors. Preferably, one coefficient is the same as, or a small multiple of, the other. Here, 55 and 79 (the coefficients of x) are not related by an integer, or a couple of small integers. On the other hand, the y-coefficients 49 and 84 have a common factor of 7, and are in the ratio 7:12, a pair of small numbers. This is why we chose to eliminate the y-variable.

The x-variable could be eliminated using 55 and -79 as multipliers of the equations. This results in larger numbers, and more chance for error. (Errors tend to creep in when computing or copying large numbers.)

Of course, any of several machine methods could be used to solve these equations, including graphing and matrix-solving functions. Here, we tried to honor the requirement to solve by elimination.

7 0

2 years ago

The populations of termites and spiders in a certain house are growing exponentially. The house contains 120 termites the day yo

zysi [14]

Answer:

in order to triple the inicial population of spiders, will take 50395 days

Step-by-step explanation:

we can define the termite population function as T(t) and the one for spiders as S(t) , where t represents time measured in days

since both have and exponencial growth

T(t)= a*e^(b*t)

S(t)= c*e^(d*t)

1) when the day the person moves in , t=0 and T(0)= 120 termites

T(0) = a*e^(b*0) = a = 120

2) after 4 days , t=4 and the house contains T(4) = 210 termites

T(4)= 120*e^(b*4) = 210 → 4*b = ln (210/120) → b = (1/4)* ln(210/120)= 0.14

therefore

T(t) = 120*e^(0.14*t)

3) 3 days after moving in , t=3, there were T(3) = 120*e^(0.14*3)=182.63≈ 182 termites . The number of spiders is half of the number of termites → S(3) = T(3) * 1 spider/ 2 termites =91.31 spiders ≈ 91 spiders

4) after 8 days of moving in , t=8, there were T(8) = 120*e^(0.14*8)=367.78≈ 368 termites . The number of spiders is 0.25 times the number of termites → S(8) = T(8) * 1 spider/ 4 termites =91.94 spiders ≈ 92 spiders

from

S(t)= c*e^(d*t) → d = ln [S (tb)/S (ta) ] / (tb-ta)

therefore d = ln [ S(8)/S(3) ] / (8 - 3 ) = 2.18*10^-5

in order to triple the initial population

S(t3) = 3 *S(0) = 3*[c*e^(d*0)] = 3*c

S(t3) = c*e^(d*t3) = 3* c → t3 = ln(3) / d = 50395 days

5 0

3 years ago

At a track samma finished the 200m race in 25.98 seconds.Tom finished the 100 meters race in 12.58 seconds.Which runner ran at t

d1i1m1o1n [39]

Answer:

tom

Step-by-step explanation:

if you look at samma's rate you can easily find that she was much slower

6 0

3 years ago

A company developed the following linear model to help budget annual expenses over time. In this model, x represents the number

ollegr [7]

The only reasonable answer I could think for this is "A.The company's expense budget for 2009 was $189,785."
I believe this because since x is the years after 2009 then you wouldn't times that by the expense budget for that year or any year eliminating B and C. When finding the total expense budget for this you would have to take in account the budget from 2009 so that would lead it to add 189,758. Since we are talking about after 2009 then D would be eliminated since 2008 is before 2009.
I hope this helps! Good luck!

6 0

3 years ago

Find the solution to the system of equations.

Rzqust [24]

Answer:

(4, 1).

Step-by-step explanation:

The solution is the coordinates of the points where the 2 lines intersect.

That is where x = 4 and y = 1.

4 0

3 years ago