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Ali and Kiana buried a treasure together on their school's field. The actual field is 400 feet wide. Ali made an 8-inch-wide map to record its location. Kiana made her map using a scale of 1 in. To 20 ft. On Kiana's map, the treasure is 2 inches from the south edge of the field. How far is the treasure from the south edge on Ali's map?

Respuesta :

Answer:

The treasure is 0.8 inches from the south edge on Ali's map.

Step-by-step explanation:

Scaling factor, f = (Original length)/(Scalet length)...(i)

Let [tex]f_1[/tex] and [tex]f_2[/tex] be the scaling factors used by Ali and Kiana respectively.

Given that the field is 400 feet= 400x12 inches wide and Ali made an 8-inch-wide map to record its location.

So, [tex]f_1 = (400\times12)/8=600[/tex]...(ii)

Kiana made her map using a scale of 1-inch to 20 feet=20x12 inches.

So, [tex]f_2=(20\times12)/1=240[/tex]...(iii)

As on Kiana's map, the treasure is 2 inches from the south edge of the field,

so, from equations (i), and (ii), the original length of the treasure for the south edge of the field

[tex]=2\times f_2[/tex]

=2x240

=480 inches

Now, again from the equation (i) and (ii), the scaled length of the treasure on Ali's map

= 480/f_1

=480/600

=0.8 inches

Hence, the treasure is 0.8 inches from the south edge on Ali's map.

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