If $x : y = 5 : 2$ $x:y = 5:2$ and $y : z = 3 : 2$ $y:z = 3:2$ , what is the ratio of $x : z$ $x:z$ ?

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If $x : y = 5 : 2$ $x:y = 5:2$ and $y : z = 3 : 2$ $y:z = 3:2$ , what is the ratio of $x : z$ $x:z$ ?

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Answer 1 · 2016-03-23T15:46:36

$\frac{x}{z} = \frac{15}{4} \to x : z = 15 : 4$ $x/z= 15/4" " ->" " x:z=15:4$

Explanation:

To solve this you need to adopt the fraction style of ratio presentation

$\frac{x}{y} = \frac{5}{2}$ $x/y=5/2$

$\frac{y}{z} = \frac{3}{2}$ $y/z=3/2$

Need $\frac{x}{z}$ $x/z$

Consider $\frac{x}{y} \times \frac{y}{z}$ $x/yxxy/z$

Write this as:

$\frac{x \times y}{y \times z}$ $(x xx y)/(yxx z)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As an example of what I am about to do consider $3 \times 2$ $3xx2$ . You have the same result if you reverse these numbers.

So $3 \times 2 = 2 \times 3 = 6$ $3xx2=2xx3=6$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So $\frac{x \times y}{y \times z} = \frac{x \times y}{z \times y} = \frac{x}{z} \times \frac{y}{y} = \frac{x}{z}$ $(x xx y)/(yxx z)" " =" "(x xx y)/(z xx y)" " =" " x/z xxy/y" " =" "x/z$

$.$ $color(white)(.)$

$\Rightarrow \frac{x}{z} = \frac{x}{y} \times \frac{y}{z} = \frac{5}{2} \times \frac{3}{2} = \frac{15}{4}$ $=>x/z=" "x/y xxy/z" " =" " 5/2xx3/2" " =" " 15/4$

Answer 2 · 2016-11-18T09:44:30

Alternative approach

$x : z \to \frac{x}{z} = \frac{15}{4}$ $x:z" "->" "x/z=15/4$

Explanation:

$\frac{x}{y} = \frac{5}{2}$ $x/y=5/2$ ..................................Equation(1)
$\frac{y}{z} = \frac{3}{2}$ $y/z=3/2$ ...................................Equation(2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From equation (2) $y = \frac{3}{2} z$ $y=3/2z$

Consider equation(1)

Substitute for y giving

$\frac{x}{y} = \frac{5}{2} \to \frac{x}{\frac{3}{2} z} = \frac{5}{2}$ $x/y=5/2 " "->" "x/(3/2z)=5/2$

$\frac{2}{3} \frac{x}{z} = \frac{5}{2}$ $2/3 x/z=5/2$

$\frac{x}{z} = \frac{3}{2} \times \frac{5}{2} = \frac{15}{4}$ $x/z=3/2xx5/2 = 15/4$

Answer 3 · 2016-11-18T14:05:01

$x : z = 15 : 4$ $x : z = 15:4$

Explanation:

Before you can compare all three values in one ratio,
make $y$ $y$ the same in both ratios:

$x : y : z$ $x" ":" "y" ":" " z$

$5 : 2 : z$ $5" ":" "2" ":" " z$
$15 : 6 : z$ $color(red)(15" ":" "6)" ":" " z$

$x : 3 : 2$ $x" ":" "3" ":" " 2$
$x : 6 : 4$ $x" ":" "color(red)(6" ":" " 4)$
$15 : 6 : z$ $color(red)(15" ":" "6)" ":" " z$

Now that we have $y$ $y$ the same in both ratios:

$15 : 6 : 4$ $color(red)(15" ":" "6" ":" " 4)$

$:. x : z = 15:4$

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If $x : y = 5 : 2$ $x:y = 5:2$ and $y : z = 3 : 2$ $y:z = 3:2$ , what is the ratio of $x : z$ $x:z$ ?

3 Answers

Explanation:

Explanation:

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If x:y = 5:2x:y=5:2x:y = 5:2 and y:z = 3:2y:z=3:2y:z = 3:2, what is the ratio of x:zx:zx:z?

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If $x : y = 5 : 2$ $x:y = 5:2$ and $y : z = 3 : 2$ $y:z = 3:2$ , what is the ratio of $x : z$ $x:z$ ?