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miskamm [114]
3 years ago
15

Savannah is 24 years older than Ryan, while Sebastian is 5 times as old as Ryan. If Savannah and Sebastian are twins, which equa

tion may be used to determine the age of all three people?
a. 8x = 24
b. 24+2x = 5x
c. 24+5x = x
d. 24+x = 5x
Mathematics
2 answers:
Gnom [1K]3 years ago
6 0

Answer:

Kim is 24 years older than Tom Kim and Tom are twins. These two statements are not compatible, unless the mother of Kim and Tom was in labor for 24 years LOL


Second statement


Savannah and Sebastian are the same age (twins)


X being Ryan's age the correct answer is 24+x = 5x


D is the correct answer


To solve 24+x= 5x


Subtract x from each side


24= 4x


Divide each side by 4


6= x


Savannah is 30 Sebastian is 30 Ryan is 6

Step-by-step explanation:


Ainat [17]3 years ago
3 0

Answer:

D

Step-by-step explanation:

Let x be Ryan's age. Savannah's age is represented by 24 + x, while Sebastian's age is represented by 5x. Since Savannah and Sebastian are the twins set their equal to each other. The answer is 24 + x = 5x.

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b must be equal to -6  for infinitely many solutions for system of equations y = 6x + b and -3 x+\frac{1}{2} y=-3

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}

Let us bring the equations in same form for sake of simplicity in comparison

\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}

Now we have two equations  

\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}

Let us first see what is requirement for system of equations have an infinite number of solutions

If  a_{1} x+b_{1} y+c_{1}=0 and a_{2} x+b_{2} y+c_{2}=0 are two equation  

\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} then the given system of equation has no infinitely many solutions.

In our case,

\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}

 As for infinitely many solutions \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}

Hence b must be equal to -6 for infinitely many solutions for system of equations y = 6x + b and  -3 x+\frac{1}{2} y=-3

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Answer:

Step-by-step explanation:

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