Question 185491
11. Start by writing the cost equation for each club.
{{{C[1] = 200+25x}}} This is the cost for Karate Klub for x months.
{{{C[2] = 100 +35x}}} This is the cost for Kool Karate for x months.
a) To find after how many months is the cost the same, set {{{C[1] = C[2]}}} and solve for x, the number of months.
{{{C[1] = C[2]}}}
{{{200+25x = 100+35x}}} Subtract 25x from both sides.
{{{200 = 100+10x}}} Now subtract 100 from both sides.
{{{100 = 10x}}} Finally, divide both sides by 10.
{{{highlight(10 = x)}}}
The cost will be the same in 10 months.
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b) To find which club is the better deal at 6 months, set x = 6 for both equations and see which one is less.
{{{C[1] = 200+25x}}} Substitute x = 6.
{{{C[1] = 200+25(6)}}}
{{{C[1] = 200+150}}}
{{{highlight(C[1] = 350)}}} Karate klub costs $350 for 6 months.
{{{C[2] = 100+35x}}} Substitute x = 6.
{{{C[2] = 100+35(6)}}}
{{{C[2] = 100+210}}}
{{{highlight(C[2] = 310)}}} Kool karate costs $310 for 6 months.
Kool Karate is less for 6 months.
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c) To find the best deal for 12 months, use part b) as a guide but set x = 12.
You can do this!