In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. in the collection there are 18 ten inch gongs. half of the gongs in the collection are tiger gongs. of the tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. half of the twelve inch gongs are not tiger gongs, and half of all gongs are fifteen inches in diameter. how many gongs are there in the collection? a. 18b. 54c. 72d. 90e. 108

Option 'E' is correct.

Step-by-step explanation:

Since we have given that

Let the total number of gongs be 'g'.

Number of ten inch gongs = 18

Let the number of 12 inch gongs be 'x'.

Let the number of 15 inch gongs be 'y'.

so, equation would be

Half of the gongs are tiger gongs is given by

Half of the 12 inch gongs are not tiger gongs

so, number of tiger gongs which is of 12 inch =

Among the tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch.

Half of the gongs are of 15 inch is given by

Since we have

so, According to question, it becomes,

Hence, Option 'e' is correct.

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.