Rina wants to run a karaoke machine for a family reunion. the prices to rent the machine from two different companies are shown . for how many days must she rent the machine for the cost from each place to be the same?
|company| deposit| cost per day|
mike's music| $5 |$1.25|
karaoke korner| $4 | $1.50~

Total pay for the year (x) = Base pay + (percentage commission)*x, where x is the number of karaoke machines sold.  Total pay (x) = $35,470 + ($1,300/machine) * (1.145)*x = $38,486. The 1.145 factor represents the unit price of each machine sold PLUS the 14.5% commission.  Let's begin solving this for x by subtracting $35,470 from both sides of this equation. The result is $3,016, which represents commission income.  Each machine sells for $1,300, and the saleswoman earns 14.5% on each sold. That comes to 1.145($1,300) = $1488.50 per machine sold.  Dividing both sides of this equation by ($1,488.50/machine), we get  $3016  x = = 2.027. Round this off to 2, representing the  $1488.50 commission earned on the sale of  2 machines.

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584