Translate the following statements directly into one or more

Translate the following statements directly into one or more equations using the symbols given. Do not try to solve for the unknowns or draw any conclusions from the given informatior If there are more than one equation, use commas to seperate them. There are one half as many quesadillas (z) as tacos (y). 20% of the total number of elliptical galaxies (x) and spiral galaxies (y) are spiral galaxies. There are six fewer wormholes (x) than black holes (y). There are three times as many white dwarfs (x) as neutron stars (y). The number of gravitons (x) is 20% of the number of Higgs bosons (y). There are four more baseball fans (x) than football fans (y). Among a total of 300 planets, some of which are gas giants (x) and the rest are not (y), 40% of the total are gas giants. Among all the planets, 600 less are earth-like worlds (x) than are not (y), and one eighth as many are earth-like worlds as are not. Among a total of 400 customers, six times as many are preferred customers (x) as are not (y).

Solution

(i) x = y/2

(ii) 20 % * (x + y) = y or, 0.2(x + y) = y

(iii) x = y - 6

(iv) x = 3y

(v) x = 20 % * y or x = 0.2y

(vi) x = y + 4

(vii) y = 300 -x , x = 40% * (x + y) or, x = 0.4(x+y)

(viii) x = y - 600 , x = y/8

(ix) x = 6 ( 400 - y)