A single ticket to the magic show costs ttt dollars, but there is a discount of 5\%5%5, percent per ticket if a group buys 101010 tickets. The expression 10t-10\cdot 0.05t10t−10⋅0.05t10, t, minus, 10, dot, 0, point, 05, t describes the total cost of buying 101010 tickets for a group.

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Step-by-step explanation:

The question isn't complete as each amount to be matched with the expression that represents its situation isn't provided

We obtain a general formula for the expressions and move forward from there.

Cost of one ticket = t dollars

Normal cost of buying n tickets for (n<10) = nt dollars

Normal cost of buying 10 tickets = 10t

But there's a discount of 5%, hence, the discount = 5% × 10t = 0.5t

Cost of buying 10 tickets = 10t - 0.5t = 9.5t dollars

Normal cost of buying n tickets for (10 < n < 20)

= (Cost of buying 10 tickets) + (cost of buying the extra tickets)

= 9.5t + (n - 10)t = nt + 9.5t - 10t = (nt - 0.5t) dollars

Cost of buying 20 tickets

= 20t - (2)(0.5t) = 20t - t = 19t dollars

Cost of buying (20 < n < 30) tickets

= nt - (2)(0.5t) = (nt - t) dollars

So, generally, cost of buying an exact k-multiple of 10 = (10kt) - (k)(0.5t) = 10kt - 0.5kt = (9.5kt) dollars

And the general price of buying n tickets, where n is associated with a k-multiple of 10 = nt - (k)(0.5t) = (nt - 0.5kt) dollars.

Basically, it's a discount of 0.5t dollars for every 10 tickets bought!

With this explanation and general formulas provided, we should be able to match any amount given with the expression that represents its situation. Thank you!

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