Question

Maths for Business

Answer 1

Answer:

Star Letter Costs: £150

Reader Letter Costs: £80

Explanation:

Represent Star Letters with S and Reader's Letters with R

Given

$3S + 8R = 1090$

$2S + 11R = 1180$

Required

Determine the value of R and S

Multiply the first equation by 2 and the second equation by 3; to eliminate S

$2(3S + 8R = 1090) => 6S + 16R = 2180$

$3 (2S + 11R = 1180) => 6S + 33R = 3540$

Subtract the resulting equations

$(6S + 16R = 2180) - (6S + 33R = 3540)$

$6S - 6S + 16R - 33R = 2180 - 3540$

$16R - 33R = 2180 - 3540$

$-17R = -1360$

Divide both sides by -17

$\frac{-17R}{-17} = \frac{-1360}{-17}$

$R = \frac{-1360}{-17}$

$R = 80$

Substitute 80 for R in the first equation

$3S + 8R = 1090$

$3S + 8 * 80 = 1090$

$3S + 640= 1090$

Subtract 640 from both sides

$3S = 1090 - 640$

$3S = 450$

Divide both sides by 3

$S = 150$

Hence:

Star Letter Costs: £150

Reader Letter Costs: £80