Identify the first 4 terms in the geometric sequence given by the explicit formula ƒ(n) = 4 × 2(n – 1).
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Answer:
33 copies were paperback and 12 were hardcover.
Step-by-step explanation:
Let h represent the number of hardcover copies and p represent the number of paperback copies.
We know that the total number of copies was 45; this gives us the equation
h+p = 45
We know that each hardcover copy is 7 ounces; this gives us the expression 7h.
We also know that each paperback copy is 5 ounces; this gives us the expression 5p.
We know that the total weight was 249 ounces; this gives us the equation
7h+5p = 249
Together we have the system
We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:
To eliminate p, we will subtract the equations:
Divide both sides by -2:
-2h/-2 = -24/-2
h = 12
There were 12 hardcover copies sold.
Substitute this into our first equation:
12+p=45
Subtract 12 from each side:
12+p-12 = 45-12
p = 33
There were 33 paperback copies sold.