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PilotLPTM [1.2K]

3 years ago

11

four friends buy tickets for two shows on consecutive nights. They use a coupon for $5 off each ticket. They pay a total of $416

for 8 tickets. Write and solve an equation to find the original price of the tickets.

2 answers:

Serjik [45]3 years ago

6 0

do u want the answer or how to solve it?

lys-0071 [83]3 years ago

6 0

Number of friends = 4

Number of tickets for 2 days = 4 x 2 = 8

Off on each ticket was $5 therefore, for 8 tickets they got a total of 8 x 5 = $40 off

Now if they payed a total of $416 for 8 tickets which is the amount after they used a coupon to get $5 off each ticket, then you must add the amount that was waived off as a discount to find the original price of the tickets. To find this, we need to add $40 to $416 to get $456.

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Answer:

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Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

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$22^{\circ} 8'6'' = 22.135^{\circ}$

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$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

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$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

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goblinko [34]

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