hello.need help on the 2 questions

tickets for a concert are available at two prices. the more expensive ticket is $30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for$1800
the more expensive ticket is 30 + x
less expensive ticket is x
10 more of the cheaper tickets than the expensive ones for $1800 10 + x ... ? the members of a club hire a bus for$2100, seven members withdraw from the club and the remaining member have to pay $10 more each to cover the cost. How many members originally agreed to go on the bus. let x be number of people so x= 2100, x-7= ... ? thank you guys 2. Originally Posted by white hello.need help on the 2 questions tickets for a concert are available at two prices. the more expensive ticket is$30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for $1800 the more expensive ticket is 30 + x less expensive ticket is x 10 more of the cheaper tickets than the expensive ones for$1800
10 + x ... ?

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Keep x as you defined it. Let y = number of expensive tickets bought for $1800. Then: Cheap tickets: 1800 = (10 + y)x => 1800 = 10x + xy .... (1) Expensive tickets: 1800 = y(x + 30) => 1800 = xy + 30y .... (2) Equate (1) and (2): 10x + xy = xy + 30y => x = 3y .... (3) Substitute (3) into (2): 1800 = 3y^2 + 30y => y^2 + 10y - 600 = 0 => (y + 30)(y - 20) = 0 etc. 3. Originally Posted by white [snip] the members of a club hire a bus for$2100, seven members withdraw from the club and the remaining member have to pay $10 more each to cover the cost. How many members originally agreed to go on the bus. let x be number of people so x= 2100, x-7= ... ? thank you guys Original cost per member$\displaystyle = \frac{2100}{x}$. New cost per member$\displaystyle = \frac{2100}{x} + 10 = \frac{2100 + 10x}{x}$. New number of members = x - 7. Therefore:$\displaystyle 2100 = (x - 7) \left( \frac{2100 + 10x}{x}\right)\displaystyle \Rightarrow 2100x = (x - 7)(2100 + 10x)\displaystyle \Rightarrow 210x = (x - 7)(210 + x)\$.

Expand the right hand side, simplify, re-arrange into the form quadratic = 0 and solve for x.

For checking purposes: I get x = 42.