Answer:
Star Letter Costs: £150
Reader Letter Costs: £80
Explanation:
Represent Star Letters with S and Reader's Letters with R
Given
[tex]3S + 8R = 1090[/tex]
[tex]2S + 11R = 1180[/tex]
Required
Determine the value of R and S
Multiply the first equation by 2 and the second equation by 3; to eliminate S
[tex]2(3S + 8R = 1090) => 6S + 16R = 2180[/tex]
[tex]3 (2S + 11R = 1180) => 6S + 33R = 3540[/tex]
Subtract the resulting equations
[tex](6S + 16R = 2180) - (6S + 33R = 3540)[/tex]
[tex]6S - 6S + 16R - 33R = 2180 - 3540[/tex]
[tex]16R - 33R = 2180 - 3540[/tex]
[tex]-17R = -1360[/tex]
Divide both sides by -17
[tex]\frac{-17R}{-17} = \frac{-1360}{-17}[/tex]
[tex]R = \frac{-1360}{-17}[/tex]
[tex]R = 80[/tex]
Substitute 80 for R in the first equation
[tex]3S + 8R = 1090[/tex]
[tex]3S + 8 * 80 = 1090[/tex]
[tex]3S + 640= 1090[/tex]
Subtract 640 from both sides
[tex]3S = 1090 - 640[/tex]
[tex]3S = 450[/tex]
Divide both sides by 3
[tex]S = 150[/tex]
Hence:
Star Letter Costs: £150
Reader Letter Costs: £80
