Samuel spent $16 for 4 erasers and 2 pencils. Alva spent $10.50 for 3 erasers and 1 pencil. How much does 5 erasers and 3 pencils cost?

$___.00

Step-by-step explanation:

Let E = Erasers and P = Pencils

4E + 2 P = $16…(1)

3E + 1P = $10.50…(2)

Multiply (2) by 2 to make Pencils in (1) and (2) equal.

6E + 2P = $21…(3)

Subtract (3) from (1) to eliminate P

2E = $5 => Erasers = $2.50 each

Substitute this value for Erasers into (3)

6 * $2.50 + 2P = $21

2P = $21 - $15 = $6 => Pencils = $3

Therefore 5 Erasers + 3 Pencils cost

5 * $2.50 + 3 * $3 = $12.50 + $9 = $21.50

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18