Question

Parent volunteers at Manchester High School are processing yearbook order forms. Students have an option to get the basic yearbook or a deluxe option, which includes engraving and a protective cover. In Mrs. Robinson's class, 19 basic yearbooks and 4 deluxe yearbooks were ordered, for a total of $1,841. The students in Mr. Yamamoto's class ordered 19 basic yearbooks and 16 deluxe yearbooks, for a total of $2,861. How much does each option cost?

Answer 1

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,

`19x+4y=1841\ldots(1)`

Also, Mr Yamamoto's purchase can be written in the equation as follows,

`19x+16y=2861\ldots(2)`

Next, substract equation (2) from equation (1) as follows,

`19x+16y-19x-4y=2861-1841`

Further, solve the obtained result as follows,

`\begin{gathered} 12y=1020 \\ y=(1020)/(12) \\ y=85 \end{gathered}`

As a result, obtained that y is equal to 85.

Furthermore, substitute y = 85 in equation (1) as follows,

`19x+4*85=1841`

Further, solve the obtained result as follows,

`\begin{gathered} 19x+340=1841 \\ 19x=1841-340 \\ 19x=1501 \\ x=(1501)/(19) \\ x=79 \end{gathered}`

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.