Question

Maths for Business

TMA Week 1
Question 1
A magazine pays different rates for Star Letters and Readers' Letters.
In June the magazine editor paid out £1090 for 3 Star Letters and 8 Readers'
Letters.
In July £1180 was paid out for 2 Star Letters and 11 Readers' Letters.
How much does the magazine pay for each type of letter?

Answer 1

Star Letter Costs: £150

Reader Letter Costs: £80

Step-by-step 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

`(-17R)/(-17) = (-1360)/(-17)`

`R = (-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