MATH SOLVE

2 months ago

Q:
# Find the ratio of x to yx/5 = 2/3 = 5/ya: 2/3b: 4/9c: 1

Accepted Solution

A:

ANSWER

[tex] \frac{x}{y} = \frac{4}{9} [/tex]

EXPLANATION

The given equation is

[tex] \frac{x}{5} = \frac{2}{3} = \frac{5}{y} [/tex]

We separate the above equation into two different equations.

[tex] \frac{x}{5} = \frac{2}{3} ...eqn1[/tex]

[tex]\frac{2}{3} = \frac{5}{y} ...eqn2[/tex]

From equation (1), we cross multiply to obtain,

[tex]3x = 10[/tex]

This implies that,

[tex]x = \frac{10}{3} [/tex]

From equation (2), we cross multiply to get,

[tex]2y = 15[/tex]

This implies that,

[tex]y = \frac{15}{2} [/tex]

We divide x by y to get,

[tex] \frac{x}{y} = \frac{ \frac{10}{3} }{ \frac{15}{2} } [/tex]

This is the same as,

[tex] \frac{x}{y} = \frac{10}{3} \div \frac{15}{2} [/tex]

[tex] \frac{x}{y} = \frac{10}{3} \times \frac{2}{15} [/tex]

[tex] \frac{x}{y} = \frac{2}{3} \times \frac{2}{3} [/tex]

[tex] \frac{x}{y} = \frac{4}{9} [/tex]

The correct answer is B

[tex] \frac{x}{y} = \frac{4}{9} [/tex]

EXPLANATION

The given equation is

[tex] \frac{x}{5} = \frac{2}{3} = \frac{5}{y} [/tex]

We separate the above equation into two different equations.

[tex] \frac{x}{5} = \frac{2}{3} ...eqn1[/tex]

[tex]\frac{2}{3} = \frac{5}{y} ...eqn2[/tex]

From equation (1), we cross multiply to obtain,

[tex]3x = 10[/tex]

This implies that,

[tex]x = \frac{10}{3} [/tex]

From equation (2), we cross multiply to get,

[tex]2y = 15[/tex]

This implies that,

[tex]y = \frac{15}{2} [/tex]

We divide x by y to get,

[tex] \frac{x}{y} = \frac{ \frac{10}{3} }{ \frac{15}{2} } [/tex]

This is the same as,

[tex] \frac{x}{y} = \frac{10}{3} \div \frac{15}{2} [/tex]

[tex] \frac{x}{y} = \frac{10}{3} \times \frac{2}{15} [/tex]

[tex] \frac{x}{y} = \frac{2}{3} \times \frac{2}{3} [/tex]

[tex] \frac{x}{y} = \frac{4}{9} [/tex]

The correct answer is B