Given that Mrs Robinson's class, 19 basic yearbooks and 4 deluxe yearbooks were ordered, for a total of $1,841.
Also, Mr Yamamoto's class ordered 19 basic yearbooks and 16 deluxe yearbooks, for a total of $2,861.
Suppose that the basic yearbook is denoted by x and deluxe yearbooks is denoted by y then Mrs Robinson's purchase can be written in the equation as follows,
[tex]19x+4y=1841\ldots(1)[/tex]Also, Mr Yamamoto's purchase can be written in the equation as follows,
[tex]19x+16y=2861\ldots(2)[/tex]Next, substract equation (2) from equation (1) as follows,
[tex]19x+16y-19x-4y=2861-1841[/tex]Further, solve the obtained result as follows,
[tex]\begin{gathered} 12y=1020 \\ y=\frac{1020}{12} \\ y=85 \end{gathered}[/tex]As a result, obtained that y is equal to 85.
Furthermore, substitute y = 85 in equation (1) as follows,
[tex]19x+4\times85=1841[/tex]Further, solve the obtained result as follows,
[tex]\begin{gathered} 19x+340=1841 \\ 19x=1841-340 \\ 19x=1501 \\ x=\frac{1501}{19} \\ x=79 \end{gathered}[/tex]As a result, obtained that the value of x is equal to 79.
Thus, the required value of the basic yearbook is 79 and the deluxe yearbook is 85.
