The number of rooms at hotel g is 10 less than twice the number of rooms at hotel h. if the total number of rooms at hotel g and hotel h is 425, what is the number of rooms at hotel g?
(a) 140
(b) 180
(c) 200
(d) 240
(e) 280

the number of rooms at Hotel G is 280

Step-by-step explanation:

Let x represent the number of rooms at hotel G.

Let y represent the number of rooms at hotel H.

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. This means that

x = 2y - 10 - - - - - - - - - - -1

If the total number of rooms at Hotel G and Hotel H is 425, it means that

x + y = 425

Substituting x = 425 - y into equation 1, it becomes

425 - y = 2y - 10

3y = 425 + 10 = 435

y = 435/3 = 145

x = 425 - y = 425 - 145

x = 280

280

Step-by-step explanation:

let the number of rooms at Hotel H=x

number of rooms at Hotel G=2x-10

now total number of rooms at Hotel G and Hotel H=x+2x-10=3x-10

but total number of rooms=425

3x-10=425

3x=425+10=435

x=435/3=145

so number of rooms at Hotel H=145

number of rooms at Hotel G=425-145=280

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step-by-step explanation:

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isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough