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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?

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 Inclu class=

Sagot :

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.

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