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A supermarket display consists of boxes of cereal. The bottom row has 63 boxes. Each row has seven fewer boxes than the row below it. The display has six rows.

(a)   Write and use a function to determine how many boxes are in the top row.

(b)   Use the appropriate formula to determine the number of boxes in the entire display.

 Apr 15, 2022
 #1
avatar+578 
+3

a)  To find the number of boxes in any row...we can use

 

an  =  63 - 7 (n - 1)      where  n  is an integer from 1 to 6 inclusive

 

So...in the 6th row, we have

 

a6  =  63 - 7(6 - 1)  =  28 boxes

 

b)  To find the total number of boxes, we can use

 

Sum  = 

 

[ Number of boxes in the first row + Number of boxes in last row ] * [ No. of rows / 2 ]

 

So we have

 

[ 63 + 28 ] * [6/2]   =

 

273 boxes in total

 

 

Used answer by CPhill for framework: https://web2.0calc.com/questions/anyone_11

 

-Vinculum

 

smileysmileysmiley

 Apr 15, 2022
 #2
avatar+2455 
+1

1) \(\color{brown}\boxed{f(x)= 63-7(x-1)}\), where \(1 \leq x \leq 6\)

 

2) There are 6 rows, the bottom row with 63 and the top row with 28. 

 

Writing as factors of 7, we have: \((7 \times 4) + (7 \times 5) + \space ... \space + (7 \times 9)\)

 

We can rewrite this as: \(7 \times (4+5 + \space ... + \space 9)\)

 

This is equal to \(7 \times 39 = \color{brown}\boxed{273}\)

 Apr 15, 2022

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