So first of all we need to write an algebraic equation for Mike. We know that he bought 3 coffees and 1 doughnut. Then the total price of these things is:
[tex]3c+1d=3c+d[/tex]And we know that he had to pay $19 so this expression is equal to 19:
[tex]3c+d=19[/tex]Then the answer to question 14 is the second option.
Bob bought one coffee and one doughnut so the total cost of his purchase is:
[tex]c+d[/tex]We know that this cost is equal to $9 so we get:
[tex]c+d=9[/tex]And the answer to question 15 is the third option.
In question2 16 and 17 we need to find c and d. For this purpose we need to use the algebraic equations for Mike and Bob:
[tex]\begin{gathered} 3c+d=19 \\ c+d=9 \end{gathered}[/tex]Let's take the second equation and substract c from both sides:
[tex]\begin{gathered} c+d-c=9-c \\ d=9-c \end{gathered}[/tex]Now we substitute this expression in place of d in the first equation:
[tex]\begin{gathered} 3c+d=3c+(9-c)=19 \\ 3c+9-c=19 \\ 2c+9=19 \end{gathered}[/tex]Now we substract 9 from both sides:
[tex]\begin{gathered} 2c+9-9=19-9 \\ 2c=10 \end{gathered}[/tex]And we divide both sides by 2:
[tex]\begin{gathered} \frac{2c}{2}=\frac{10}{2} \\ c=5 \end{gathered}[/tex]Then the price of one coffee is $5 so the answer to question 16 is the third option.
Now we are going to take the equation for Bob and take c=5:
[tex]c+d=5+d=9[/tex]If we substract 5 from both sides we get:
[tex]\begin{gathered} 5+d-5=9-5 \\ d=4 \end{gathered}[/tex]Then the price of one doughnut is $4 and the answer to question 17 is the second option.
