Parent volunteers at Centerville 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. McKee's class, 11 basic yearbooks and 25 deluxe yearbooks were ordered, for a total of $3,045. The students in Mr. Stephenson's class ordered 2 basic yearbooks and 22 deluxe yearbooks, for a total of $2,142. How much does each option cost?
Let's assume the cost of a basic yearbook is $x and the cost of a deluxe yearbook is $y.
Based on the information provided, the following equations can be formed:
11x + 25y = 3045 ........(1)
2x + 22y = 2142 ........(2)
To solve these equations, we can use the method of substitution.
From equation (2), we can express x in terms of y:
2x = 2142 - 22y
x = (2142 - 22y)/2
Substituting this value of x in equation (1), we get:
11(2142 - 22y)/2 + 25y = 3045
Multiply through by 2 to eliminate the fraction:
11(2142 - 22y) + 50y = 6090
Multiply and distribute:
23562 - 242y + 50y = 6090
Combine like terms:
-192y = -17472
Divide through by -192:
y = (-17472)/(-192)
y = 91
Substituting this value of y in equation (2), we get:
2x + 22(91) = 2142
2x + 2002 = 2142
Subtract 2002 from both sides:
2x = 140
Divide through by 2:
x = 70
Therefore, the basic yearbook costs $70 and the deluxe yearbook costs $91.