Question

Each of the variables t, w, x, y, and z represents a different positive real number. Given the equations below, which of the 4 variables w, x, y, and z necessarily has the greatest value?

1.23w = t
1.01x = t
0.99y = t
0.23z = t

Answer 1

z has the largest value

Explanation:

w = t/1.23

x = t/1.01

y = t/.99

z = t/.23

If the numerator is the same for a fraction, the larger the number for the denominator, the smaller the fraction (ex: 1/3 < 1/2, 1/5 > 1/7)

t/1.23 < t/1.01 < t/.99 < t/.23

w < x < y < z

Answer 2

Greatest values is of z which corresponds to z =
`\displaystyle(t)/(0.23)`

Explanation:

In the given question, we have some variables that have a positive real value.

The given variable are:

t

w

x

y

z

We have to find the greatest value out of the w, x, y, z.

Now,

`1.23w = t\\\\w = \displaystyle(t)/(1.23)`

`1.01x= t\\\\x = \displaystyle(t)/(1.01)`

`0.99y = t\\\\y = \displaystyle(t)/(0.99)`

`0.23z = t\\\\z = \displaystyle(t)/(0.23)`

Larger the denominator, smaller is the number and smaller the denominator, greater is the number.

So, the greatest values is of z which corresponds to z =
`\displaystyle(t)/(0.23)`