Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
We have two equations.
Let M be the Michaela's age and J the Jake's age.
The first one is that Michaela's age is ten years more than half the age of Jake.
[tex]M=\frac{J}{2}+10[/tex]The second equation can be written knowing that the sum of the two ages is 55:
[tex]M+J=55[/tex]We can start by substituting J in the first equation, using the information of the second equation:
[tex]\begin{gathered} J=55-M \\ M=\frac{J}{2}+10=\frac{(55-M)}{2}+10=\frac{55}{2}-\frac{M}{2}+10=\frac{75}{2}-\frac{M}{2} \\ M=\frac{75}{2}-\frac{M}{2} \\ M+\frac{M}{2}=\frac{75}{2} \\ \frac{3}{2}M=\frac{75}{2} \\ 3M=75 \\ M=\frac{75}{3} \\ M=25 \end{gathered}[/tex]The age of Michaela is 25 years.
7) Lets call
H: the number of atoms of hydrogen
C: the number of atoms of carbon
O: number of atoms of oxygen
We know that there are twice as many atoms of hydrogen as oxygen. This means that if we have 2 oxygens, we should have 4 hydrogens.
This can be written as:
[tex]H=2O[/tex]We know that one more atom of carbon than hydrogen.
This is:
[tex]C=H+1[/tex]We know that the sum of atoms is 21. This is:
[tex]H+C+O=21[/tex]Now that we have 3 equations for the three unknowns we start by solving for C.
We use the substitution method to solve it.
[tex]C=H+1\longrightarrow H=C-1[/tex][tex]H=2O=C-1\longrightarrow O=\frac{C}{2}-\frac{1}{2}[/tex]Then, we can replace H and O in the 3rd equation:
[tex]\begin{gathered} H+C+O=21 \\ (C-1)+C+(\frac{C}{2}-\frac{1}{2})=21 \\ (1+1+\frac{1}{2})C-1-\frac{1}{2}=21 \\ \frac{5}{2}C-\frac{3}{2}=21 \\ \frac{5}{2}C=21+\frac{3}{2}=\frac{42+3}{2}=\frac{45}{2} \\ \frac{5C}{2}=\frac{45}{2} \\ C=\frac{45}{2}\cdot\frac{2}{5}=9 \end{gathered}[/tex]The numbers of atoms of carbon is 9 atoms.
Alternative method:
Atoms of hydrogen = 2 * atoms of oxygen
Atoms of hydorgen = atoms of carbon - 1
Then we can say that:
Atoms of hydrogen = 2 * atoms of oxygen = atoms of carbon -1
Then, from the last equation:
Atoms of oxygen = (1/2)*atoms of carbon - (1/2)
If we add all the atoms, we get 21 atoms:
Atoms of hydrogen + Atoms of oxygen +Atoms of carbon = 21
We will replace each of the types of atoms for an expression where the atoms of carbon are present, because is what we need for our answer.
We will call x the number of atoms of carbon.
As:
Atoms of hydrogen = atoms of carbon - 1 = x-1
Atoms of oxygen = (1/2)*atoms of carbon - (1/2) = 1/2*x-1/2
We will have:
[tex]\begin{gathered} Atomsofhydrogen+Atomsofoxygen+Atomsofcarbon=21 \\ (x-1)+(\frac{1}{2}x-\frac{1}{2})+x=21 \\ x-1+\frac{1}{2}x-\frac{1}{2}+x=21 \\ (x+\frac{1}{2}x+x)-1-\frac{1}{2}=21 \\ \frac{5}{2}x-\frac{3}{2}=21 \\ \frac{5}{2}x=21+\frac{3}{2}=\frac{21\cdot2+3}{2}=\frac{42+3}{2}=\frac{45}{2} \\ x=\frac{45}{2}\cdot\frac{2}{5}=9 \end{gathered}[/tex]x, the number of atoms of carbon, is equal to 9.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
