Question

Jim goes to the movies every Friday night with his friends. Last week they bought 25 adult tickets and 40 youth tickets at total cost of $620. This week, they spend $560 on 30 adult and 25 youth tickets. what's the cost of one adult and one youth ticket?

Answer 1

`"adult "=$12" and youth "=$8`

Explanation:

`"let x be the cost of and adult ticket and"`

`"y be the cost of a youth ticket"`

`25x+40y=620to(1)`

`30x+25y=560to(2)`

`"we can simplify the values by dividing both equations"`
`"by 5"`

`(1)to5x+8y=124to(3)`

`(2)to6x+5y=112to(4)`

`"to eliminate x multiply "(3)" by 6 and "(4)" by 5"`

`(3)to30x+48y=744to(5)`

`(4)to30x+25y=560to(6)`

`"subtract term by term to eliminate x"`

`(5)-(6)`

`(30x-30x)+(48y-25y)=(744-560)`

`rArr23y=184`

`rArry=184/23=8larrcolor(red)"cost of youth ticket"`

`"substitute "y=8" in equation"(3)`

`(3)to5x+64=124`

`rArr5x=124-64=60`

`rArrx=60/5=12larrcolor(red)"cost of adult ticket"`

`color(blue)"As a check"`

`(1)to(25xx12)+(40xx8)=300+320=620" correct"`

`(2)to(30xx12)+(25xx8)=360+200=560" correct"`

Answer 2

The cost of one adult and one youth ticket are `$12 and $8`
respectively.

Explanation:

Let `A` be the cost of single adult ticket and `Y` be the cost of

single youth ticket , Then `25A+40Y=620` or

`5A+8Y=124 (1)` and `30A+25Y=560` or

`6A+5Y=112 (2)`.Multiplying equation (1) by `6` and

equation (2) by `5` we get `30A+48Y=744 (3)` and

`30A+25Y=560 (4)` Subtracting equation (4) from

equation (3) we get `23Y=184 or Y=8` Substituting `Y=8`

in equation (1) we get `5A +8*8=124 :. 5A =124-64` or

`5A=60 :. A=60/5=12 :. A=12 and Y=8`.

The cost of one adult and one youth ticket are `$12 and $8`

respectively. [Ans]